While we're at it, he wasn't a fan of public displays if faith either
And when you pray, do not be like the hypocrites, for they love to pray standing in the synagogues and on the street corners to be seen by others. Truly I tell you, they have received their reward in full. But when you pray, go into your room, close the door and pray to your Father, who is unseen.
They clearly don't believe in Jesus. At this point they are just pretending to be Christians and destroying it from within, at least in the US. American-style Christianity still hasn't spread everywhere, yet.
They believe in the Jesus their pastor tells them about. They don't read the Bible.
But I'm not going to call them fake Christians. That's a 'no true Scotsman.' They worship Christ, so they are Christians. It doesn't matter that they don't worship the Jesus of the Bible. The Jesus of the Bible was fictional anyway.
I am not the one calling them fake Christians, God did
James 2:10 "For whoever keeps the whole law but fails in one point has become guilty of all of it." The Bible said to take care of the poor and sick, fairly simple commandment, and they are failing to follow it.
It's not like jesus is super rightwing sometimes. This is like saying I'm a batman fan despite my idea of batman being a guy who fights with a katana and shoots lasers from his toes because no true Scotsman
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.