I think this is a complicated, grey area.
redpepper and I took (a second time) a parenting course a while back. One of the concept taught is the idea of classifying problems/issues/people's actions into 2 categories, and approaching these two kinds of issues separately. I think the same concept can be applied to relationships between adults - just change "kid" to "partner"
category 1 - "kid issue"
category 2 - "family issue"
A kid issue is basically defined as an issue that really affects only the child. These are the issues that one needs to let go of. Good examples are what clothes they wear - if they want to wear two different coloured socks, who cares? It doesn't hurt anyone else
A family issue is one that affects others in a negative way, or one that has huge consequences that would be devestating for the child. Brushing teeth is a family issue, because it has huge health consequences. So is if the child is throwing rocks at someone, because it negatively affects another.
Now, the concept needs some modification to apply to adults in relationships. I think one can look at all of one's partners actions, and classify them as a "partner issue" (eg, they stay up all night talking with their other partner, and so are exhausted the next day, which is not something you would do), or classify it as an "family issue".
Things which you consider "family issues" - rate the seriousness of it. So if your partner for example said something rude to their other partner, which you would not tolerate, but are confident that the two of them can deal with it themselves and they will sort it out, then this is a mild family issue. You wouldn't accept it, you don't like it, but they can likely sort it out themselves. Perhaps this is worth letting go of.
Moving up the scale of seriousness, maybe your partner keeps staying up all night to talk with their other partner, and so keeps cancelling your time together. Perhaps this is something which needs to be discussed and can't be left. This is a bigger family issue.
Even more serious family issues where you really need to step in is when everyone's safety is at risk, eg, sexual health. Or if there is emotional or otherwise violence between your partner and that person's partner. Or when their actions with their other partner is really going to jepordize your relationship.
So in summary I guess my thoughs are:
1. Let go of what is not a huge issue for them and doesn't affect you much.
2. For things which are bigger issues, look at the severity, how much it affects you, and what the chances they will sort it out themselves
All that said, if my partner is treating me and their other partner without a similar level of respect, I would wonder why and what is going on.