I actually recently had a conversation with a ladyfriend about something similar.
I have one ladyfriend (S) that I've seen for almost two years now and I just recently started seeing the second ladyfriend (M).
M said she was nervous because she felt like she had to be "approved" by S before she was allowed into my life in a romantic way. I explained to her that that wasnt how we ran things. S has the right to an opinion about the people I see and I give that opinion very serious consideration and weight. If I introduce her to someone I'm seeing and she has a problem, we talk about it and I find out why she has that problem.
If her concerns are legitimate and well-founded, based on a problem I hadn't seen and backed up with concrete examples, chances are excellent I'll stop seeing that new person. S has not demanded I stop seeing them, she had problems based on very real and identifiable points of reference that I likely would also have had problems with had I seen them first.
S does not, however, have the right to make demands or ultimatums. She cannot say "Stop seeing her or we're through." She has no right or ability to control my actions. This goes for both of us; I have no right to demand she do or not do anything and I cannot control her actions. If I am determined to do something she absolutely cannot abide by, she can say "I cannot stay with you if you do that, I have to leave for my own well-being."
It seems like six of one, half dozen of the other but there's an important distinction; one is using what power you have to make a threat to get what you want, the other is informing the other person of a situation you cannot endorse and have to remove yourself from for your own good.
In that way, we avoid a hierarchical situation where the needs of one person are constantly put before another's and we maintain an equal relationship. Neither of us controls the other and we dont leverage the emotional bond we have to manipulate the other.
Being an anarchist (big A and little a), I tend to shun hierarchy wherever its found. Wherever there is a power differential, wherever someone has more power and someone else has less, there is hierarchy and it will exacerbate with time. Power tends to concentrate and consolidate as time goes by unless that is deliberately counteracted by the people involved in the system, whatever the system may be. Hierarchy can be traced to the root of virtually any problem you'd care to name and as such I dont feel we should allow it in ANY context.
I have no personal direct experience with things like children, large-scale finances, or ownership of property but I do know of alternate models that can keep the power differential to a minimum. I can recognize there is sometimes a need for a hierarchical structure there because of the society we live in, but I feel that is a very last resort as many problems can be solved collectively without having to resort such an obviously faulty idea.
I am as direct as a T-Rex with 'roid rage and about as subtle. It isn't intended to cause upset, I just prefer to talk plain. There are plenty of other people here who do the nice, polite thing much better than I can. I'm what you'd call a "problem dinner guest."