Well as the current rules are written out, it's pretty much like that. Bearers of a Tailed Beast are acknowledged as some of the most active and strongest people in many ways. And as such, they receive a sort of high-ground to dictate who they choose to RP with. And since there is much RP involving them, then that dictation expands quite a bit sometimes. Though that doesn't mean they can flat-out deny anyone due to certain abilities the challenger could have. The rules also state that there has to be good logical reasoning as to why they can deny a challenge, or otherwise face stripping.
It's a very fickle game to play when listing out one's challenge preferences and denying a challenger a match, when they are entitled to address all challenges they receive.
Likewise, a village kage has the same power of preferences as well. Though on a much wider scale and range, due to them being an authoritative figure. But they bare a larger stake, as what they dictate is acceptable or not can influence not only themselves, but also their shinobi and villagers. It can even cause some to leave, and change allegiance to someone who is more accepting of things here and there. This can in turn, give them less authority. Though at the same time, they can be used as references as to what is considered to be too outrageous or outlandish. Perhaps there should be a sort of preferences that each village has. Village RP preferences, similar to a Jinchuriki's challenge preferences. But that's a topic for another thread.