How can the ritual slaughtering of an animal Shabbat be kosher? TB Khullin 14

Immediately the Mishnah on today’s daf TB Khullin 14 is problematic “In the case of one who slaughters an animal on Shabbat or on Yom Kippur, although he is liable to receive the death penalty, his slaughter is valid.” (Sefaria.com translation) The very first Tosafot on the page ד"ה השוחט בשבת raises the following problem. Who else would purposely desecrate the Sabbath but a  Jewish heretic (מוּמָר). We have previously learned Tb Khullin 5a that we are forbidden to eat ritually slaughter animals by a Jewish heretic who desecrates the Shabbat.

There are different categories of Jewish heretics. The first category is a transgressor with regard to only one matter (מְשׁוּמָד לְדָבָר אֶחָד). This person accepts the Torah however, he doesn’t want to observe a commandment, for example he really loves his BLT sandwiches. The second category is a transgressor who rejects the entire Torah (מְשׁוּמָד לְכׇל הַתּוֹרָה כּוּלָהּ). The last category is a transgressor who becomes an idolater (מְשׁוּמָד לַעֲבוֹדָה זָרָה). One who desecrates the Sabbath is considered like a transgressor who rejects the entire Torah. Consequently, how can this Mishnah teach that his slaughter is valid?

The Tosafot provides two possible solutions. The Mishnah is dealing with the case of a person who slaughters the animal on Shabbat in private. One who privately desecrates the Sabbath isn’t considered a Jewish heretic (מוּמָר). If this person would slaughter the animal publicly, we would be forbidden to eat the meat. The second solution is this person’s first time offense. A first-time offender isn’t considered a Jewish heretic; consequently, even though he’s guilty of a death sentence his ritually slaughtering of animal is kosher. Once he becomes a habitual offender he is considered a Jewish heretic and his ritual slaughtering is no longer kosher.

Rambam solves the problem by interpreting the person slaughter the animal unintentionally transgressed (שׁוֹגֵג). Either he didn’t know that slaughtering an animal on Shabbat is forbidden or he didn’t realize that that day was Shabbat. If the person ritually slaughter the animal on Shabbat on purpose, he is considered a Jewish heretic and the slaughter becomes invalid.