I think neutral tag doesn't prevent anyone from joining a campaign, rather it will help the hiring manager to make the right selection of users to be accepted.
...A neutral tag is neutral and should be treated as such.
I know I've read on Service sub-board where a manager was asking selected members to get their neutral tag issues resolved or get removed from a campaign they already were on. I don't know why a manager would do that or consider a neutral tag to be anything sinister because that's not the way the community saw it a few years ago. I don't know if things have changed now. Besides, I know of a member who runs loan services here and uses neutral tags for those he lends money to and not as something bad. So, would such a campaign manager then base their conclusion on all neutral tags being for a wrongdoing? But of course, no. Screening hunters out based on neutral tag is a wrong call.