Equatorial bulge and tectonic plates
The plates are not as rigid as you think. You seem to be imagining the situation as something like this: I boil an egg and take the shell off in pieces, but I can't take a piece of shell from the end and make it lay flat on the side of the egg. However, rock is not that rigid on scales of thousands of kilometres and millions of years (I don't think there exists any material which would be that rigid). Also, Earth's equatorial bulge is tiny relative to its diameter -- less than 50km. Tectonic plates move very slowly, and there is plenty of time for them to deform as they move.