As you can see by my profile pic, I was in the same boat.
Protection
For me personally, I used -35dB plugs and -28dB earmuffs on top of eachother, and still my T grew louder throughout the last 16 months of my playing (ocasionally with personal practise, mostly with gigs). So to answer your first question, it's definitely possible.
As for forms of protection: The cheap, foamy earplugs and good earmuffs (3M, Peltors for example) are by far the best at cancelling noise. 'Musician made' earplugs and IEM's, are really good at keeping the tones of music somewhat natural, while offering 'OK for most people' amount of protection. But because drummer's don't need tones, unless you're singing of course, I'd suggest going for maximum protection instead.
The most safe solution I could think of is to do this:
A. You play in a band that uses full in ear monitoring (IEM)
B. You use a (good) electronic drum kit
C. You still wear earmufs and earplugs as described above
D. Your source of monitoring is the music produced by the speakers facing the crowd.
E. Avoid any stages where you're forced to play on an acoustic kit.
But of course, you can take many steps before going with the above plan. This is far from the ideal playing experience.
'Keeping up'
Also, as to why some drummers keep up: there's lots of genetics to tinnitus, and thus age of onset and severity can vary heavily from person to person. They may not have T at all, they may have it slightly after 20 years of playing after 1 loud gig without plugs (very common), they may develop it severely @age 18 despite maximum protection (me). They also can just be very stubborn and 'keep going'. Therefore, your own experience with drumming and protection's affect on your T and your mental state, is your best source for making a decision.
As Greg said, anything tinnitus is abnormal, and you should keep it on your mind for sure. Not like all the time of course, the more you think about T, the worse it gets. If I were you, I'd either make plans to quit while your T is still bearable*, or find a way to significantly reduce volume while playing the drums, and see how things go then.
Final advice
Also, if anyone 'depends' on you playing with or for them, make sure to inform them about your situation. For me personally, I quit the drums very abruptly after it overpowering the TV (1 week before drum 'exams', 4 weeks before quite a large gig): Of course, my band members, family and many others were not pleased. Having people be angry at you and as a result mocking and belittling your condition and yourself, doesn't help in coping with T. That mess almost drove me to suicide 2.5 months ago; try to prevent that, be open.
Secondly, T can indeed be very bothersome. But still, drumming can you give one a lot of joy, so do think twice before giving it up.
That's my advice, hope it helps and all the best!
*If at any point, you feel 'forced' to quit acutely, because T became unbearable, quit the drums (at least temporarily). And trust me on this (and many others on this forum), after a few months, it will once again become bearable, and you can live your life like anyone else on this planet.