The majority of good players can play in numerous different formations. It's not like 3421 requires specialised players all over the field as the spine is largely the same. A top striker in 3421 will be fine in other formations. The two #10's at Sporting were apparently one recognised #10 and one inverted winger. The two central midfielders are largely the same. The central defender won't have too much difference, and the wider central defenders will generally be fine either as a central defender or a well-balanced fullback (think Shaw or Mazraoui) in a 4 at the back system. And obviously a keeper is a keeper.
It's really only the wider areas where it becomes a bit more specialised. A top wingback may not be good enough defensively to play at fullback or good enough offensively to play at winger at the top level. And on the flip-side, it's only the inverted goal-scoring winger that arguably may not have a spot in 3421. Perhaps one, but not two.
So yes, if we completely build our squad for 3421 and then later want to change to a 433 or 4231 system then we may need to make a few changes to the squad. But it won't be a complete rebuild, and generally any new manager joining a club will make a few changes to suit the specifics of what he wants anyway.
The more important aspect of having consistency between managers is style of play, not formation. High defensive line or low? Dominate possession or counter-attack? Hard pressing from the front or look to win the ball more in midfield? Build up with lots of short fast passing or spread the play by long balls out wide? Etc. They won't all be exactly the same, but that's where the consistency needs to be. Most players who suit doing those things in one formation will still suit doing them in another.