(6) The following individuals do not have a portion in the world to come...the Minim, the Epicursim, those who deny the Torah, those who deny the resurrection of the dead and the coming of the [Messianic] redeemer, those who rebel [against God], those who cause the many to sin, those who separate themselves from the community, those who proudly commit sins in public as Jehoyakim did, those who betray Jews to gentile authorities, those who cast fear upon the people for reasons other than the service of God, murderers, slanderers...

It is proper, however, to say this in justification of those Jewish scholars who deal with this subject. Every Israelite is obliged to believe that everything that is found in the Torah is absolutely true, and any one who denies anything that is found in the Torah, knowing that it is the opinion of the Torah, is an unbeliever; as the Rabbis say in chapter Chelek, that anyone who says, the whole Torah emanates from the Divine except one verse, which Moses said on his own authority, is liable to the imputation charged in the biblical expression, Because he hath despised the word of the Lord, and is classed among those who deny the divine nature of the Torah. But a person who upholds the law of Moses and believes in its principles, but when he undertakes to investigate these matters with his reason and scrutinizes the texts, is misled by his speculation and interprets a given principle otherwise than it is taken to mean at first sight; or denies the principle because he thinks that it does not represent a sound theory which the Torah obliges us to believe...or entertains a certain notion in relation to one of the miracles of the Torah because he thinks that he is not thereby denying any of the doctrines which it is obligatory upon us to believe by the authority of the Torah,—a person of this sort is not an unbeliever. He is classed with the sages and pious men of Israel, though he holds erroneous theories. His sin is due to error and requires atonement...

This seems to be the correct view as held by the Rabbis of the Talmud...But the one whose intention is not to rebel, nor to depart from the truth, nor to deny what is in the Torah, nor reject tradition, but whose sole intention is to interpret the texts according to their opinion, though they interpret them erroneously, is neither a heretic nor an unbeliever.

[The observance of] the Sabbath and [the prohibition against] worshiping false deities are each equivalent to [the observance] of all the mitzvot of the Torah. And the Sabbath is the eternal sign between the Holy One, blessed be He, and us.
For this reason, whoever transgresses the other mitzvot is considered to be one of the wicked of Israel, but a person who desecrates the Sabbath publicly is considered as an idolater. Both of them are considered to be equivalent to gentiles in all regards.

A Jew who is an apostate because of his transgression of a particular transgression who is an expert slaughterer may slaughter as an initial and preferred option. A Jew of acceptable repute must check the knife and afterwards give it to this apostate to slaughter with, for it can be presumed that he will not trouble himself to check [the knife].
If, by contrast, he was an apostate because of worship of false deities, one who violates the Sabbath in public, or a heretic who denies the Torah and [the prophecy of] Moses our teacher, as we explained in Hilchot Teshuvah, he is considered as a gentile and [an animal] he slaughters is a nevelah.

These Tzadukkim, Beotosim, their disciples and all that err, following their path, who do not believe in the Oral Law - their slaughter is forbidden. If, however, they slaughtered [an animal] in our presence, it is permitted. For their slaughter is forbidden only because it is possible they blunder. Since they do not believe in the laws of ritual slaughter, we do not accept their word when they say, "We did not blunder."

(2) For this reason, unlearned people should not be designated as witnesses, nor do we accept such a person's testimony unless it has been established that he observes the mitzvot, performs acts of kindness, conducts himself in an upright manner, and contributes to society. The testimony of such a person may be accepted even though he is unlearned and is unfamiliar with both the Written and Oral Law.

(3) Thus one may conclude any Torah scholar may be assumed to be acceptable as a witness unless he is disqualified, and any unlearned person may be assumed to be unacceptable unless it is established that he follows just paths.

The matter needs investigation, why is the shechita of a Tzadukki valid when it is done in our presence, and is not unconditionally invalid like an Epicurus, whose status is like a Non-Jew? It seems, that Rambam's intention is to only validate those who are disciples of Tzadok, because they are like captured children ("tinokos shenishbah"), and they are considered compelled in their denial. In other words, Rambam distinguishes between an Epicurus whose status is like a Non-Jew, whose shechita is invalid on a Torah-level, as opposed to the disciples of Tzadok and Beitus, whose shechita is prohibited because we suspect maybe they did it incorrectly, but they are not invalid like that of a Non-Jew. It is clear from Rambam that only an intentional Epicurus is invalid for shechita like a Non-Jew, and not an inattentive Epicurus. His reasoning is that what invalidates the shechita isn't the label of Epicurus per se, but the wickedness of the persn, and therefore only an intentional Epicurus is intrinsically invalid. Similarly, Rambam codifies regarding what invalidates witnesses (Testimony 11:10), Our Sages had no need to list informers, epicursim, and apostates among those who are not acceptable as witnesses. For they listed only the wicked among the Jewish people. These rebellious deserters of the faith are inferior to Non-Jews...the pious among them will receive a share in the world to come. These...will not receive a portion in the world to come." What emerges according to the type of Epicurus described there who is intrinsically invalid as a witness is an intentional one [note: see Rambam there for more details], and not an inattentive one, because what invalidates a witness is the wickedness of the person, that is due to intentionally choosing to be an Epicurus, as opposed to the label or status of being an Epicurus, which includes even the inattentive one.

A person who violates a commandment of the Torah is called a transgressor, and is liable to the penalty prescribed in the Torah for that commandment. But he is not excluded from those who profess the Torah, and is not regarded as a denier of the Torah who has no share in the world to come; unless his violation of the commandment is due to the fact that he doubts whether it is a command of God, given to Moses on Sinai, or not. If this is his attitude he falls into the class of those who deny the divine origin of the Torah, as the Rabbis of the Talmud explain in chapter Chelek (Sanhedrin ch. 10). All the commandments of the Torah are alike in this respect. The command to send away the mother bird is as important as any other. If we should count specific commandments as dogmas by reason of the last consideration, we should have as many principles as there are commandments.

You asked from me regarding principles of religion, which count do I agree with? Rambam, or that of Chesdai, or of Rav Yosef Albo [Sefer HaIkkarim]?

Response: My perspective is not to concur with anything that would put our Holistic-Torah into any principle, because all of it is fundamental directly from the Almighty, and our Sages have said (Sanhedrin, Chelek), "any who say that the entire Torah is Divine except for one verse etc." And therefore, every single mitzvah is a principle and foundational. There are "light" mitzvos, that have purpose and concealed value which we can't conceive. If so, how can we cay that this one is supplementary and another is primary?

The general concept was written about beautifully by Rav Yitzchak Abravanel z"l, in his work Rosh Amanah, see there...and this is also my view, that all the details of the Torah and all its particulars are principles and foundational and primary, and one who denies them is a non-believer, who has no share in the world to come.

For this reason, if they attempt to force someone to transgress any of the mitzvos of the Torah, to make them declare that they were not commanded by Hashem on this matter, or that it was only for a limited duration of time, but now has been negated, he should accept martyrdom and not transgress. We only say transgress and don't be a martyr regarding Shabbos, that if they tell him to violate Shabbos to violate your religion [he should violate Shabbos]. And the Ritva z"l writes this as well...

(3) To whom does the above apply [they are not considered part of the Jewish people]? To a person who denied the Oral Law consciously, according to his perception of things. He follows after his insubstantial perspective and his capricious heart and denies the Oral Law first, as did Tzadok and Beitus and those who erred in following them. The children of these errant people and their grandchildren whose parents led them away and they were born among these Karaities and raised according to their conception, they are considered as a children captured and raised by them. Such a child may not be conscientious to follow the path of mitzvot, for it is as if he was compelled not to. Even if later, he hears that he is Jewish and saw Jews and their faith, he is still considered as one who was compelled against observance, for he was raised according to their mistaken path. This applies to those who we mentioned who follow the erroneous Karaite path of their ancestors. Therefore it is appropriate to motivate them to teshuva and draw them to the power of the Torah with words of peace.