The disagreements in the Tory party are fundamental and deep.
Yes Labour will have policy debates, as they did under Blair - remember Corbyn's lot were always popping up then too. But small factions are not the issue.
Currently the Tories are so ideologically split. They threw off a lot of moderates at the last election but that has made their party much less appealing electorally. They do not know whether to go centre-right, one-nation or to go full Braverman. They can't do both at the same time.
Brexit was a useful sticking plaster to keep the two sides together but it was always discussed pre-2016 that if/once the referendum went their way, the splits would worsen not improve.