Why make exceptions in this way?
The US was, and is, a deeply religious country, and a significant number of people who emigrated to the then-colonies did so in part or in whole to escape religious persecution from their homeland. While freedom of speech probably encompasses freedom of worship, the extra explicitness was added just to reinforce that the concern was being addressed.
And, to be perfectly honest, I have full confidence that any lawyer worth his salt could argue that religious belief is not speech, per se, but rather bluh bluh bluh and therefore not covered. At the very least, without that explicit clause you could probably create a state church and have other religions be second-class citizens, as long as they are tolerated to a certain extent. By explicitly forbidding a state church, they prevent the first-among-equals conundrum from becoming institutional.