I know it's important to find a HV partner but regardless of how HV both people in a relationship are, one wanting kids and another not wanting kids is often not negotiable. Should we hence avoid dating men of occupations which involve working with children (eg. primary/secondary school teacher, child psychologist, pediatrician) if we don't want kids?

Yes, a lot of people pick their careers based on salary, job security, and how easy it will be to find a job as opposed to their interests (and unfortunately some men want to work with kids as they are pedophiles), but I guess some men want to work with kids as they love kids. I assume a lot of these men also want kids of their own. It's not that different from how most veterinarians probably like animals to some extent and probably already have or want pets.