The phrase "deep rift" refers to a significant disagreement or division between people or groups that goes beyond just a regular disagreement. It suggests a serious and lasting conflict or separation. Full definition
They found that issues which once caused deep rifts between churches have been largely resolved. (religion-online.org)
Wineman's intervention sent panic through the Tory party and opened deep rifts in the Jewish hierarchy, a large part of which is desperate for Cameron to win next year's election. (theguardian.com)
The migration crisis — Europe's worst since World War II — has caused deep rifts between EU member states and left the bloc's Schengen system of open borders on the brink of collapse. (nigeriapoliticsonline.com)