"Race" is to "racism" as "religion" is to what?
Solution 1:
The term I would use is "religious intolerance." To describe the basis for events like the Inquisition in Spain.
Solution 2:
Sectarian is probably the right word for the job. (though it usually refers to opposing forces within a group).
Note that in some cases, people identify their ethnicity as the religion (jews for instance), in which case, "racism" and "religious bigotry" are nearly equivalent.