Okay, thanks for the clarification.
I can’t speak for every woman clearly. But honestly, to address your first question, that really sounds like fear-mongering more than anything. I know a fairly large number of people who are in poly relationships and I’ve honestly not sat around in conversation with any of them and heard men or women discussing losing respect for one another due to fear of their partner loving someone else more than their primary partner. What I have heard is this:
1. In the beginning we had very open and honest and vulnerable conversations about how this might happen and if it did, is this something we could handle?
2. Who were we open to accepting into our relationship? Did we want it to be simply sexual or were we open to emotional connections?
3. Did we want to remain primary partners or would everyone be equal?
These are all things that absolutely should be discussed long before anyone even considers taking on another person into their bed much less their relationship. And if not, this is where your questions likely would come into okay.

To be further honest, what you’re talking about really sounds more like what happens when cheating occurs in monogamous relationships or even poly relationships than what happens when truly open, honest, and vulnerable communication occurs between consenting parties.
Just my two cents and thoughts from my experiences within this type of relationship.

But things happen differently of course in different relationships for sure. Whomever’s work you read Re:your last statement sounds like they probably weren’t being completely honest with one another and probably had some stuff going on beneath the surface they should have been working on before diving into poly/open relationships.
Because the bottom line is always this:: it will NEVER fix a troubled relationship. If there are issues, that’s gotta be worked on first.