I'd like to resurrect this thread, as there's no solution posted yet. When I try to push a branch from Databricks, I am receiving 

Error pushing changes. Remote ref update was rejected. Make sure you have write access to this remote repository.

My repo is located on gitlab.com. Setup:

• In the Databricks Linked account settings, I've tried Git `username` as my corporate email in Gitlab. I've also tried `username` as my GitLab account name
• In the Databricks Linked account settings, I've tried `GitLab` and `Gitlab Enterprise Edition` as the Git provider.
• In the Databricks Admin settings, I have enabled "Restrict Clone, Commit & Push to allowed Git repositories" and set the URL allow list to "https://gitlab.com"
• My HTTPS GitLab token has `read_repository, write_repository` scopes with a Maintainer role.

Like OP, I can `git pull` the successfully but `push` fails. On the Databricks clone of the repo, all I have done is create a test file with one line in the root directory and update an existing file in the root directory with a single uncommented line. Please help!