Of course people can pick sides. That doesn’t mean you should denigate those (the majority of authorities, including virtually all authorities in the last 500 years!) who believe in it. But one is certainly entitled to side with those who reject gilgulim. (I say this though I personally believe in them.)
Google “trusting the torah’s sages” aishdas and you’ll find a pdf of some very interesting essays by Rav S.R. Hirsch discussing one’s obligations in hashkafa.