Other religions do tend to crawl out of the woodwork eventually.
Right now religion is mostly spread through imperial state religion, so the ruling family of empires typically dictate the faith of the galaxy.
New empires get the following religion:
- The one which the current star has (50% of the time)
- The same as their parents (40%)
- A random one (10%)
The next update will have factions rising in the game, and they will include religious factions who spread depending on faith of surrounding stars, and can either succeed in convincing the empire to switch state religion, or simply split out to form their own. It sounds similar to what you are suggesting!