In my experience, if you take Religious Texts, and spread just to your own 4-city tradition empire, assuming that your cities are nice and compact, you'll be able to hold your religion in those 4 cities even on Deity. The AI sends their missionary spam first to civs that have not founded a religion (and of course to city-states) to avoid the "stop sending missionaries to me" diplomatic penalty. Of course, if the AI hates you anyway (you're warmongering, your army is the pits, or you denounced them), then all bets are off, and expect a missionary spam.
On Deity, I find that this is good enough to hold me over until the industrial era, which is the best time to start spreading my religion with great prophets. Of course, by then you'll need prophets, as your missionaries will have negligible effect and will cost too much anyway. But that's the point: the missionaries cost too much for the AI also, and so their missionary spam will have run out of steam. Meanwhile, they've exhausted several great prophets in their own religious battles, and are now on their 5th or 6th prophets, which also cost a lot of faith. On the other hand, you saved your 3rd and 4th prophets for this purpose, so you can convert 8 cities relatively cheaply.
Granted, since it's now the industrial era, this has to be weighed against saving your faith for great engineer/scientist or some other great person.
On Deity, I find that this is good enough to hold me over until the industrial era, which is the best time to start spreading my religion with great prophets. Of course, by then you'll need prophets, as your missionaries will have negligible effect and will cost too much anyway. But that's the point: the missionaries cost too much for the AI also, and so their missionary spam will have run out of steam. Meanwhile, they've exhausted several great prophets in their own religious battles, and are now on their 5th or 6th prophets, which also cost a lot of faith. On the other hand, you saved your 3rd and 4th prophets for this purpose, so you can convert 8 cities relatively cheaply.
Granted, since it's now the industrial era, this has to be weighed against saving your faith for great engineer/scientist or some other great person.