Civilization – Why can’t I use the great prophet to enhance the religion

One thing to keep in mind is that any major religion is superior to no religion at all. Yes, it gives a bonus to your opponent, but it gives a larger bonus to your city. Therefore, its advisable to use these GPs to spread religion to cities that do not have, and are unlikely to get, Shinto. Island colonies far from other cities are the best example. They would not otherwise get a religion, so it can be wise to spread buddhism or confucianism there.

Finally, look at the benefits provided by those religions. If you have a specialty city, it may be useful to add a specialty religion. For example, if you have a pure production city, and Buddhism gives the 15 percent production bonus, it may be wise to spread Buddhism there in order to get said bonus.

Station an inquisitor/inquisitors in your city/cities and he will be unable to act. Alternatively you should be able to surround the city with 6 workers/other non-combats (triangle units) and he won't be able to get close enough to use his ability.

If he does successfully convert some citizens, you can use an inquisitor to remove his influence, but its preferable to block him by just stationing the inquisitor there.

I don't believe any of those will cause a diplomatic hit. If one of them does, it would be using the inquisitor to remove influence after the GP is used on a city.