It's normal for toddlers to be very enthusiastic about something, to the point that adults might call it obsessive. Kids that age are very much into repetitive activity - they find comfort and security in routines.
I can't speak for the environment in your home, but toddlers learn to perform if they know they will get a lot of praise for doing something.
Try slowly eliminating the hygiene episodes from his routine. Can you anticipate trigger points in his day when he's more likely to want to get up and wash his hands? If so, you can try altering your routine slightly to be busy with another activity that could distract him from feeling the urge.
You can also try simple re-directs, as in "let's play with trucks now, and we will wash your hands before we leave for the park." If he gets upset, give him a few minutes to compose himself; during that time, you start playing with the trucks.
Give each elimination at least several days -- longer if he's having trouble adjusting -- before taking another one away, and alternate between eliminating the hand-washing and teeth-brushing, so you're not taking too much away at once. If this is still an issue when he's a little older, you can explain that he only needs to brush his teeth after a meal.
Our pedi's philosophy is pretty simple: Does the behavior physically harm him in any way? If it starts to hurt him, he'll probably stop doing it. If it hurts him and he keeps doing it anyway, that's the time to bring it up with his doc.
Behavioral disorders are usually hereditary, sometimes environmental, but it's difficult and rare to diagnose much earlier than 5 y.o.
Good luck!