for people who discriminate on the basis of religion?
Like racists, only not.
Well?
Theists? 
I just use the term intolerant, I can’t say that I have heard of a word that means that specifically.
“Religious bigot” is the term that comes to mind.
FordPrefect, the same (joking) answer had occured to me.
Thank you, Diogenes! For some reason “bigot” to me had always meant a more sort of general intolerance; like you could be a bigot about everything. Not just religion.
Someone might wish to propose Fundamentalist, but I would argue against that usage. While a Fundamentalist certainly has a clearly defined definition of the correctness of their religious views, I have known many Fundamentalists who have not held the closed-minded perspective that any differing views were selected from perverse or wicked motives or that their own views were unassailable. (The fact that a certain number of Fundamentalists loudly display a certain amount of bigotry is not sufficient to make the terms interchangeable; there are Fundamentalists who are moderate in their approach to the world and their are other religious persons (progressives, liberals, or whatever term one might apply to them) who can be quite stridently bigoted in their views.
I think that (religious) bigot is probably the best term for the OP’s question.
or Atheists?
Since the word “bigot” has extended its meaning beyond religion, you could use the ohrase “religious bigot”. Sometimes there isn’t a single word for what you want to describe.
Sectarian???
Zealot works too. It is derived from “a member of an ancient Jewish sect in Judea in the first century who fought to the death against the Romans and who killed or persecuted Jews who collaborated with the Romans” (Princeton).
Only if you mean strong atheists, us weak atheists don’t discriminate. 
It’s obvious that a new word must be coined…
So take the usual anti-discrimination affirmation - “We do not discriminate by race, sex, or creed…”
So the opposite would be…
Racist
Sexist
and CREEDIST!
Thank you! Takes a bow!