mik5,
The Chazon Ish paskened as you wrote. Rav Moshe paskened as wrote (although Rav Moshe acknowledged that many erliche talmidei chachomim disagreed with him). If you hold, like Rav Moshe and the Chazon Ish, that shaking a woman’s hand is an issur d’oraisa then of course you are right.
But if you hold that m’ikur hadin shaking a woman’s hand is not an issur d’oraisa and/or is mutar altogether, then hefsed mamon or hefsed merubah can be a basis for allowing it.
You might ask “if it is mutar why do you need the hefsed altogether?” The answer is that notwithstanding the ikur hadin in America one should be machmir like Rav Moshe under normal circumstances. But if there is a situation of hefsed most morai horaah in America will be meikil.
“Nowadays you can get a Rav to say just about anything and give any sort of heter for any sort of nonsense.”
That is ridiculous. If you “heter-shop,” maybe. But I am not talking about finding the one Rav in town that will matir something. I am talking the most likely answer you will receive. I personally learned the gedarim of shaking hands from my rebbe long before it ever became nogeiah (pardon the pun) l’maaseh.
Halacha, in our days without a Sanhedrin, is determined by the consensus of morei horaah. There are many piskei halacha from the Chazon Ish that are not followed by the vast majority of Talmidei Chachomim. There are many piskei halacha from Rav Moshe that are not followed by the vast majority of Talmidei Chachomim. And there are issues for which there is no widespread consensus, where there are multiple camps with different shittos. Ask your rav for your own personal shailos, but don’t impune the frumkeit of others when they are just following the psak they received from their rav or their rabbeim.