Is an undergraduate thesis a requirement to get into grad school?
No, it's not necessary. 

Of course, all other things being equal, writing a (good) undergraduate thesis can only help. It demonstrates research capability and independence, and you'll probably get a more detailed letter of recommendation than you would from a professor who you saw only in class. But a similar argument can be made for many extracurricular activities, and you don't have time to do everything.

If you choose to write a thesis, do so because you are interested in the challenge and the topic, not because you are afraid not writing one will prevent you from getting into graduate school.