The connection between monetary policy and inflation is weak. But the connection between how the monetary system is structured and an ever increasing money supply is clear and factual.
Some MMT theorists suspect rising rates is at least not price deflationary as is assumed by Keynesian monetary theory. And the basis is simple: An increase in debt interest has to be serviced by money creation. So the tool used to reduce bank lending creates money, and increasing bank lending creates money. Both roads lead to the money printer.
The following points are taken from https://www.reddit.com/r/mmt_economics/comments/wchq55/raisi...
1. When central banks raise interest rates, this means governments spend more on their interest payments. This translates into increased income for bondholders. Higher incomes lead to more consumer demand, pushing up prices. Similarly, banks benefit from higher interest payments from the Federal Reserve. In other words, the interest from the higher interest rates goes to someone in the economy, and their demand increases rather than decreasing.
2. Interest rates are a cost for businesses. When central banks raise interest rates, businesses pass this new cost on to consumers in the form of higher prices, which is inflation by definition.
3. Higher interest rates make it harder to start a business and harder to hold inventory. This reduces supply, leading to higher prices aka inflation.
4. Finally, MMT economists point to the fact that there is no empirical research at all showing that higher interest rates decrease inflation. In fact, the correlation runs in the opposite direction.