Do your opponents gain the benefit of a religion you found?

Solution 1:

It depends whether it's a founder belief or a follower belief. If it's a founder belief, only the founder civilization gets the benefit. If it's a follower belief, every city in which there's a majority for that religion gets the benefit.

You can see whether a belief is a founder or follower belief when you select them, and also in the religion overview panel.

In your example, Guruship is a follower belief, so it applies to all cities with majority rule of that religion, regardless if they belong to the religion's founder or not. That mean that it doesn't actually benefit the founder in any way, if its not their city.

So what is the benefit of spreading a religion?

1. You get the benefit of the founder belief, which is usually better the more (global) followers you have.
2. You prevent the other civ from gaining benefits from their founder belief.
3. Civilization following your religion will be friendlier towards you.
4. City states following the religion will have their influence with you decay at a lower rate.
5. City states will often also request that your religion will be spread to them as a quest.