I think my mistake in this thread was I used too much complexity in my original post by including Jesus, religion, etc. Here is the simplification of the argument:

Teacher: "For your final essay, you can choose any topic that belongs to Category A."
Subject X belongs to category B.
Therefore the student cannot write a paper on subject X


This is a fallacy because subject X may also belong to Category A. I just didn't know the name of the fallacy. I still think its a fallacy of exclusion, but perhaps Vagabond is correct. :)

I think it's the fallacy of exclusion? I just read about it.

Hmmm, I don't think it's a slippery slope, but I get what you are saying. To me it seems similar (but not identical) to the four terms fallacy.

But for this argument we are accepting the premise that "I should stay out of politics" as true.

Let's accept that premise. We can change the subject away from religion (for simplicity), and use an example of a student at school.

Teacher: "For your final essay, you can only choose any topic that belongs to Category A."
Subject X belongs to category B.
Therefore the student cannot write a paper on subject X

What the fallacy leaves out is that Subject X belongs to both categories and so while both premises are true, the conclusion is false. Is this still a non-sequitur?