Concept of mutual reception in synastry
Nothing in one chart rules anything in another chart, they are separate charts derived from separate skies. The involved charts can be delineated separately to determine what each entails for strengths on their own but neither chart planets have any rulerships over any signs from another chart. The outside planets are placed around the base chart houses according to the framework of the base chart and the aspects they make to the base chart's planets are what are used. Just as transiting planets are placed over a natal chart, the separate sky transiting planets don't rule any signs in the natal chart, nor do the natal chart planets rule any transiting planet signs. The accidental placement strength from an outside planet in a base chart house, if any, would have some bearing on the base chart as to its expression but through according to what the outer chart planet entails from its own chart delineation and the conditions of the base chart's houses.
I don’t know if there is such a thing as mutual reception in synastry, but I've wondered something similar. I had a bad experience dating someone with Mars in Libra, and I have Venus in Scorpio, so I’ve wondered if there was something like “mutual detrimentation” between us. Lol.
My guess is that two people with planets in the signs of each other’s rulership would at least notice an affinity with each other.
My understanding is that planets in mutual reception help one another. So even if there is no such thing as mutual reception in synastry, you might see a similar effect if one person has a planet debilitated and the other person has that same planet dignified.
From my own experience, I have Mercury in detriment in Sagittarius and my husband has Mercury in rulership in Gemini. I tend to think about the big picture and the future. Details are not my forte. My husband naturally thinks about the here and now, what we need to do just to get through the week, and the details (which I consider trivia). It’s great for me because I have someone to go to for help. His Mercury helps makes up for what I lack. I notice it in our interactions every single day. The help only goes one way, however. It’s not mutual in the way mutual reception is...
I hope that's not too far off topic.