When I was an LEA appointed governor, no-one asked me what my political affiliations were. Nor my religious affiliations (which might have been relevant, given that the school in question was a Church of England Controlled School).
Indeed. My experience of being a school governor is that the whole business of ensuring that the governing body is properly "balanced" can get rather complicated. It's necessary for everyone involved to be sensitive to the wishes of parents, teaching staff, the head teacher, interested local...