In order to properly use MPS with Git, there needs to be a .gitignore file that excludes the generated files. A sample .gitignore can be found here and has to be put into the project root folder:
workspace.xml
junitvmwatcher*.properties
build.properties
# generated java classes and java source files
# manually add any custom artifacts that can't be generated from the models
classes_gen
source_gen
source_gen.caches
# generated test code and test results
test_gen
test_gen.caches
TEST-*.xml
junit*.properties