Whether or not to fight inflation is a political choice, since it is a redistribution choice
Today, inflation is hurting wage earners and bondholders. If central banks were to fight inflation strongly by raising interest rates significantly, they would favour these two categories of economic agents at the expense of borrowers (governments, companies, home buyers, and also at the expense of equity and real estate owners). The question for central banks is therefore what group of economic agents they want to protect. The Federal Reserve seems to have changed its mind on this in the recent period.