Just checked the teshuvos in Reb Moshe, and in at least two of them he says that frum people (yirei shamayim) who do shake hands hold that it is not derech chiba and we should be dan them lchaf zchus. However, he finds it hard to rely on this heter. He says I don’t see a contradiction to the fact that I was matir buses, because there it is not derech chiba for just about everybody.
(Please note that your writing makes it seem like Reb Moshe is screaming that shaking hands is terrible, and NOT comparable to buses, etc. However, the actual language is much more gentle and understanding, and clearly there is what to rely on for another Rov to pasken differently. It is all a matter of judgment as to how much derech chiba there is in a handshake. He doesn’t say asur lismoch al zeh or chas vshalom lismoch al zeh. He says kasheh lismoch al zeh.)
In social settings, it is much easier to avoid, (like make sure you are carrying a hot plate of chulent or even chopped liver in your hands at all times, so nobody will want to get near you). However, on a business interview or mtg, it is much harder to avoid (even if you excuse yourself for religious reasons), and may cause bad feelings like this guy is a really strict, unfriendly fellow and hard to get along with. With eating kosher, it seems people are much more understanding and do not take it as unfriendly. This is just my observation.
However, I do see a reason to be machmir, because if one lets down his guard too much, then it may lead to touching where it is derech chiba. It is much easier to tell people negia is always assur, rather than making subtle distinctions that it is assur if there is derech chiba and permitted otherwise. Simple rules are easier to follow than leaving it up to people’s judgment in each situation, because where do you draw the line.