By their very nature, religions tend to be inimical to democracy. The stronger the religion is, the more control it has over the culture and the government, the less democratic a country is.
A true democracy represents the will of the people, the values of a consensus of the people. But religions aren't like that. They represent a fixed set of morals, written in stone (in fact in the case of Judaism/Christianity they are LITERALLY written in stone!) These values are interpreted by a class of clergy who represent only themselves or their political affiliates, so that religion can keep people in control. This is just how religion works! I believe it's one of the reasons religion even still exists.
So, for instance, in the US a good majority of The People are Pro Choice. The largest church--which keeps insisting it's the 'official' church--is Pro Life. If this church had more political power it would impose its Pro Life value on the rest of us. And there might even be severe penalties for premarital sex or homosexuality, etc. These are not democratic values because they are not based on a consensus of The People but on some arbitrary interpretation of scripture. Which could change at any time based on the political considerations of the clergy.
To answer your question--the religions that are the biggest threats to democracy are those that are the most politically powerful. Christianity in the US, Islam in certain Middle Eastern countries (Iran, Pakistan, et al) and Judaism in Israel.