The rates that the FOMC sets for practical purposes do have a direct effect on the money supply, short term yields, short term interest rates and the strength of the dollar. Raised high enough they have caused recessions, crashed the stock market, and triggered global financial problems.
So yes, the Federal Reserve does manipulate the markets, something Conservatives should be against.
I’m no fan of gnomes twitteling the knobs. Nor their ability to effectively manage the economy. (I’ve never worked in that field)
I have a lot more confidence in mature privately held business owners. (rare breed today) I worked for 2 such companies for 35 years.