That make you go "Hmm..." until you think about them for a few seconds. The fact FDR implemented progressive social policies isn't why the 22nd Amendment was ratified. Washington, Jefferson, Madison, Monroe, and Jackson established a convention of a maximum two terms by declining to run for a third.

Just like a lot of laws, the 22nd Amendment was written when someone finally violated a long-observed norm. Four terms in a row (without a definite end, even, as Roosevelt died early in his fourth term) was wildly outside the norm and forced politicians to confront formal term limits instead of unspoken, honors system ones.

The only states that voted to reject the 22nd were Oklahoma and Massachusetts.

Congress was more partisan, mainly being Republicans and southern Democrats voting in favor. This was pre-Southern Strategy, and the GOP was more complicated. With Truman (FDR's former VP) on the backfoot when Congress was deciding on the 22nd, it's pretty obvious why there'd be a partisan split—with the amendment existing because of FDR, whose popularity the Democratic Party were still riding off of.