UJM- Hmm… I wonder if that’s true. At the end of the first perek of Yevamos, it says that even though Beis Shamai declared some keilim as tamei, and Beis Hill declared those same keilim as tahor, they still loaned things to one another. The meforshim explain, it’s because they had mutual respect for each other’s opinions, and Beis Shammai trusted Beis Hillel that BH would never loan BS a kli that BS considered tamei, even if BH themselves found nothing wrong with it (the parallel here is that someone who only eats Chalav Yisroel should be able to trust that their Chalav Stam neighbor would never serve them Chalav stam).
But the meforshim say nothign about the reverse… would BS lend BH a kli that BS considered tamei even if BH considered them tahor? Would BS respect BH enough to allow them to be meikil, and to even be a part of that kula, when they themselves hold it’s a problem? I always assumed that BS would have no problem doing this but I could be wrong.