Can you not have mutations or be in a secret society?


I have been reading up on Paranoia a bit, though it’s really hard to figure out what information I am allowed to have and what information I’m not. I want to get into a game, but I don’t like the idea of belonging to a secret society or having any mutant powers. Is there an option to simply not be a mutant and/or not belong to any of the secret societies? And if I have to, are there any consequences to just not doing any of the secondary objectives my secret society wants me to, or not using my mutant powers?