Nope!  I'm not sexist, but only dudes should be busting ghosts.
Did you intend this to mean that women should not be employed in that job?
Yes, I did say that.
There is no objective reason why women cannot do certain jobs, since well-qualified candidates have been able to meet all of the requirements for work such as firefighting regardless of their sex.  If you have a reason why no woman would be able to work as a ghost buster, you should let people know, otherwise it just sounds like you're pre-judging women based on their sex.