Is it more difficult for men to obtain female dominated jobs?

I don’t think it makes any difference. Know that they tend to be lower paid. For a long time women were only allowed to be in certain kind (my dad told me I could be a secretary or a teacher, although I guess he would have added bookkeeper or nurse if he’d thought of it). It seems like history to young people, but it wasn’t to a lot of today’s parents! Few men applied, partly because the pay was low (they were “women’s jobs”, and not meant to support a family in the thinking of the time). It is changing, but fewer men still apply.