EAGLE stores files in autogenerated-XMLlike format, meaning that while Git is capable of attempting a merge of files, the end result will likely be invalid. Thus, you need to avoid merging different versions of files with conflicting changes together.
In order to configure git for electronics, you must ensure your .gitignore and .gitattributes are configured correctly. This page includes the files you need to place in your repository. You also need to switch your merge command habits to prevent Git from attempting to merge files which are incapable of merging.
Please ensure the following files are placed in the root of your EAGLE project repo before making an initial commit. (or at least as soon as possible)
Download by clicking the download button in the header of each file.
For all merges between branches, use one of the following commands:
git merge -X theirs <branch-to-merge-in>
to merge the branch in, overwriting any files which may conflict on the branch being merged into (probably what you want), or
git merge -X ours <branch-to-merge-in>
to merge the branch in, discarding any changes made in the branch being merged into which conflict
You must use these commands, or Git will attempt to merge different parts of your EAGLE files, which will not work as stated above.