They're not immune to political pressure. They really should be raising rates again (housing prices going up, stock market at all time highs, inflation still not under control) and aren't for exactly that reason.
That said they operate with very little political interference in recent years which is part of why the greenback has such strength. If that were to change the USD/Economy would be in a world of pain. All of a sudden those deficits would be much more crippling as people wouldn't trust the currency.
The other side of the coin is that if the Fed hiked now, half the country would be up in arms that the Fed basically assassinated the Biden administration. I think the Fed is not in the wrong of waiting a bit, at least until after the elections. Then if inflation starts coming off, well there's nothing for them to do, and if it doesn't, they can do it without so much fuss from politicians.
Hell, if Trump wins, he might be in the lucky position of claiming that he singlehandedly fixed everything and allowed the Fed to start cutting rates :D
This is not an if, it has already been happening for many, many months.