Not a logical fallacy. Anyone can claim they worship Christ, but all religion have obligations that if you don't follow you are clearly not a follower.
No one can follow everything in the Bible. It contradicts itself all over the place.
No one can follow "feed the hungry, heal the sick, and house the houseless"? I understand if it was some contradictory command, but this one clearly isn't.
I will give an example from Islam since I am more familiar with it. Alcohol is prohibited in Islam yet some people claim to be Muslims and consume it. Those people fall under one of two, no third:
They know they are committing a sin and feel bad about it.
Deny they are committing a sin.
Those who are group 1, are still Muslims but sinners, but group 2 are out out out!
So those who don't to feed the hungry and deny the obligation, aren't Christian.
It is a fallacy, just not a formal fallacy. It is within the purview of informal fallacies. An informal fallacy is found in the content of the argument itself, not its logical structure. The "no true Scotsman" fallacy occurs when the standards for a category are arbitrary, irrelevant, or are established in an ad hoc manner purely to win the argument.
You can be a part of a group with strict tenets, and be a hypocrite that follows none of it too. After all, you cannot be a hypocrite of something without having placed yourself within the group or set of tenets of which you are hypocritically not following. Thus you can be a Christian, and a hypocrite. You can say that, you are either a hypocrite or a Christian, and that's all well and good too, but perhaps that's a different argument. In language, you can specify the group or set of tenets one is a hypocrite of. Thus these are Christian hypocrites. Just as there are probably a few Muslim Hypocrites too.
I see the point you are trying to make and it has some merit. However, I think there is also merit in distinguishing between like people who say they are Christian but don't follow anything from the Bible and people who say they are Christian and do.
Like, you can point to most shapes and say "that's a polygon" but sometimes it's more helpful to say "that's a triangle", "that's a square", and "that's juat a line, not a polygon actually "
Per my metaphor, it's a polygon. That is, Christianity. But the "don't feed the poor" subset are like a triangle versus the "we should feed the poor" are an octogon. Both polygons. Very different.
I don't know what "triangle" maps back to in the context of Christianity. "Heterodox" or "heretical" aren't precise enough.
The term used in Islamic jurisprudence for someone who claims to believe in a religion but doesn't follow it is munafiq i.e. hypocrite. I don't know what it is called in Christianity/English. But since Islam borrows a lot of concepts, some literally such as shaheed being literal translation from Greek: martyr, and I have heard Christian Arabs use "munafiq", I would think the Greek word for it will be related to hypocrisy.