'爱好是什么' can mean '취미가 무엇입니까?' or '취미가 뭐에요?' '취미가 뭘여요?' is not correct because '뭘' is a short form of '무엇을', and it can be an object in a sentence. Likewise, '뭐' is a short form of '무엇' which can be a subject with subject markers like '은/는/이/가 or an object putting '을/를' as in '무엇'. '취미가 뭐여요?' is understandable but sounds wierd and it's like a dialect. 在中文上，'무엇,무엇이,무엇을' 都是 ‘什么'. That's why it makes you confused, I guess.

Difference between 뭐 and 뭘 : 뭐 = short form of 무엇 (what, interrogative pronoun) 뭘 = short form of 무엇을 (what + particle [or: postposition] 을/를) [N.B. 을/를 is a marker for a DIRECT OBJECT in general.]) (There are so many concepts of variations involved in "요 form" conjugation. Hence, let us concentrate on solely the verb "to be" [이다].) In present affirmative and interrogative forms, the verb 이다 can be respectively expressed as, 1) 니다 form: 입니다 (affirmative) / 입니까? (interrogative); 2) 　요 form: 　예요 (affirmative) / 　예요? (interrogative) [when preceding term is a vowel]; 3) 　요 form: 이에요 (affirmative) / 이에요? (interrogative) [when preceding term is a consonant]. And for your particular question, it is given as, "What is your hobby?" = (당신은 / 너는) 취미가 뭐예요? As you may see, the question contains no direct object of interest, especially on the interrogative pronoun 뭐. Thus, the use of marker 을/를 is NOT appropriate in such case; which means, the question cannot be expressed as something like, "(당신은 / 너는) 취미가 뭘이에요?". --- Good weekend. / 좋은 주말을. / 祝　週末愉快。