I personally don’t think that there is any protocol outright prohibiting relationships between anyone, the protocol would be against anyone using power to force someone into a relationship. For instance if Kathryn wanted a relationship with Chakotay she could start one unless she knew he might have objections to a relationship and then she would have to wait for him to make the first move. Actually Chakotay was pretty negative about ship board relationships in the episode “Elogium”.
I think it is possible that members of Starfleet personal in relationships were strongly encouraged to remain loyal to those relationships while on long term missions. By this I mean that Janeway being engaged to Mark Johnson would be required to wait until Mark Johnson broke the relationship before she could began another one.
Whatever the ruling, I think it would be based on ethics and not on rank.