A levi wasn’t circumcised because his parents are intactivists. Does the Rosh Yeshiva allow such a person to read from the Torah? Could they have the levi aliyah? Can they wash the kohen for birkat kohanim?
The basic pesak is that someone who does not have a brit milah, even if he is מומר לערלות, is only considered to be a mumar for one aveirah. He does not have a larger status of pasul. See Shulchan Arukh YD 2:7. (The one exception might be whether he can be a mohel, see Rema in Shulchan Arukh YD 264:1.) There is a debate in the poskim about whether this applies to someone who is not doing it merely because he is afraid of the pain. Certainly it does not apply to a person who is not doing it because he is afraid he might die or something similar (see Beit Yosef YD 2, Shakh YD 2:21, Darkhei Teshuva YD 2:94). So he might not even be in the category of mumar.
Since we allow people who do aveirot to do all those things that you mentioned, this person can do them as well, even if he is in the category of mumar. Though, he can’t eat a korban Pesach.