With all respect to Abacus, that is not always the case, nor should the OP accept it as such.
It’s perfectly possible to get a job, but your choices will not be as varied as a non-Asian foreigner. First off, yes, you will be discriminated against for the simple fact that you look Taiwanese. You want to get it out in the open from the beginning that you are not white and see if the school has a problem with that so you won’t waste any of your time. Some schools will flat out tell you that they want a white foreigner. No big deal, just move on. Other schools are open towards non-white foreign teachers but will try to scam you by offering you only a Chinese teacher’s salary and making you do more work. Others give you a salary above a Chinese teacher’s but below a foreign teacher’s. Don’t accept this. Demand to be treated as a “real” foreign teacher or you’ll regret it further down the road.
Obviously, this cuts down on your choices quite a bit, so it won’t be as easy for you to find a good job compared to white foreigners, but it’s definitely possible. So don’t settle for less. Just respect yourself and you will find a cram school that respects you.
Best of luck.