Inflation is an extreme handout to the wealthy.
Money is by definition zero sum, otherwise the word "inflation" would have no meaning. There are good questions around what an over leveraged loan is, but fundamentally, the supply of money is to some degree fixed at any given moment.
The wealthy and powerful keep their money in tax benefited, inflation tracking assets. Many of those assets are stocks, and a major business cost is labor. Wages are generally not inflation tracking. That amplifies the benefit of inflation to the wealthy. So the buying power lost by suppressed wages and devalued savings, as well as the devaluing of all money currently in flight such as paychecks, is exactly gained by those with wealth/ownership. Inflation also makes loan's cheaper to pay off, further benefiting those with enough assets to get a loan.
When the market stagnates or companies freeze hiring or do mass layoffs, it puts employees in an even worse negotiating position resulting in even more suppressed wages past the first order effect of inflation.
So what's even better for the rich than tax breaks is inflation.
The fed is the beating heart of the economy, it pumps money through its sluices.
The fed is in many ways the Balrog deep in Moria.
Oligarchs do answer to other oligarchs, even if they don't answer to law, and there's a good chance that many of them see the impending potential disaster of either stagflation -- people won't have enough money to buy goods and the economy stalls and maybe doesn't restart, or hyperinflation -- the definitive end of American hegemony as countries move to a different reserve currency and America is no longer able to fund its military. The economy is also directly tied, if not most directly tied, to the legitimacy of the ruling regime, so a policy of choosing loyalists over qualifications or letting it be corrupted by someone selling out tomorrow for today is likely to lead to actual civil unrest instead of performative civil unrest.
My guess is that the finance business oligarchs see it as a red line because the moment the fed is corrupted, it's no longer their fed, but Trump's fed, and that will be equivalent to the moment Putin gathered all of Russia's oligarchs, with one of them in a diminutive cage in a court room, and then said "half" and held out his ring with the implication of the power relationship being clear (part of the greater story of the Magnitsky act).
It's also worth noting that normally you would get capital flight once the wealthy get scared, but the US has told every foreign country that American citizens in that country are under American jurisdiction and therefore all wealth must be reported to the US government, so while in the past an oligarch might have been happy to cause civil unrest with their unchecked greed, America's deep financial reach means that many will pay a hefty price, if they are even allowed exfiltrate the majority of their fortunes at all, binding them to the outcome of fed decisions as well.
But I'm very far from an expert, so probably wrong about some of that.