Nothing changed about the religion belief-wise, what changed was the focus of presentation.
Vatican II changed how Catholics share the faith with others because many people now have an ahistorical view of religion, Christianity and a relative view of truth. So it was implemented to open the doors to the world and more effectively share the faith.
Unfortunately this was implemented during the 60’s and instead of implementing Vatican II people pretty much did what they wanted, instead of listening to the Church even Priests and Bishops just sometimes did whatever they wanted and we ended up with a kinda mess.
Read what the documents of Vatican II say and it will really shed some light on things. Some are kinda wordy and take a bit to read but it is very useful.
The rift is pretty complicated, as there are actually about 4 positions…
The people who don’t want any change at all and just want to get rid of Vatican II, probably because of all the abuses.
The people who understand that truth doesn’t change and just want an honest implementation.
(these two in the middle are pretty close)
The people who might misunderstand Vatican II as a way of making the Church modern and more flexible with truth.
(yes it was made to improve the sharing of the faith)
The people who use Vatican II to do what they want to do and change the Church
Read the documents and it will help a lot.