I would only agree if those 'specialities' would be sensible, having suicide bombers for Islam is like having a 'anti-condom' unit for Catholicism that has the special ability to infect your cities with AIDS... or 'dishonest merchants' for Judaism...
Let's make those bonuses reasonable, it's a worthy discussion as modding would make that possible despite Firaxis decision.
Each religion should have a 'combat' unit because each religion had some fighting in it's time. Each religion should also get a peaceful bonus because no religion is only devoted to war.
The controversial religions:
Christianity:
Unique unit:crusader/templar. Does not only symbolise those who attacked middle east but cloistered knights in general, Christianity supported knight orders very much.
Bonus:better missionaries, Christianity was most active in converting others.
Islam:
Unique unit:certainly not a bomber, rather than that, a 'fanatic' from the medieval period. Hashishin would fit in nicely, a Dervish, a 'Ghazi' soldier or something like that.
During the crusades there were religous warriors on both sides.
Bonus:religous buildings require no upkeep or even give you extra income. That's because Islam requires it's followers to give tithes.
Alternatively they could have a bonus to assimilation as Islam says it's enough to
say aloud that your Muslim to join the religion, in many wars peple saved their lives that way.
Buddhism:
Unit:warrior monk, most Buddhists are pacifists but in turbulent times in Asia bands of warrior monks were a force to be reckoned with, and as far as i know they weren't much better than other religions 'fanatics'.
Bonus:better culture production. Buddhism is popular across the world despite not being a state religion nowhere.
Hinduism:
units:a warrior from an elite caste, don't know what they are called. They would be strong but come in very limited numbers, one per each big city maybe.
bonus:not sure, growth rate? better temples?
Polytheism of European variety, Greeks, Vikings, Gauls, Romans...
units:no special units but a bigger chance to get a great leader trough fighting as heroic values are treasured.
bonus:normal temples are cheaper because people don't need much to start worshipping. 'Pagans' are easier to conver because the idea of a new god is ok for them.
Confucianism
units:no idea
bonus:AFK a science bonus would be appropriate as Confucianists value wisdom.
Tribal religions, Animism
unit:tribal warriors, an upgrade to the basic warrior that has upgraded defense, later would be fodder.
bonus

ne happy face in each city, people worship without a need of temples.
Judaism
unit:Macabee or Zealot, possibly Judaism would allow you to draft Zealots in time of dire need.
bonus:the 'chosen people':lesser corruption, much worse at converting others, harder to convert themselves.
Daoism:
Don't know much about it.
Shinto:
Not an expert.
If Protesthantism would be available it should give you less corruption or a productivity bonus but you could not build temples for happines.