I've been using git for I guess 15 years, on a variety of server platforms (github, atlassian, MS devops, plain ssh) and branching models, with teams of various sizes, and I've never had a repo "break". Branching and merging is what git is amazing at.

The worse thing I've had happen is that someone was lazy when merging and just did a "take mine" on 100s of files, thinking that they'd do a "proper" merge later. Of course git doesn't work like that and their lazy merge had to unwound very carefully.