It is my understanding that he was non-politically aligned and willing to run on either ticket. The choice came down to his desire to see a strong NATO and UN, and his belief that the GOP was most likely to oppose both, but not if their leader (POTUS) was firmly in the pro camp. Basically, he ran as a Republican because he had less in common with them than the Democrats...
Sure, Truman was willing to step down in 1948 in favor of Ike. But the fact is that Eisenhower was neither a liberal nor a Democrat, which is why he chose the GOP.