Just done a fresh install of WordPress 5.1 and Ultimate Member 2.036 and getting same issue on updating profile & cover image.
Steps to recreate:
1. Edit Profile
2. Click ‘Upload Photo’ or change cover photo (Modal form appears)
3. Select photo/image
4. Click the ‘Apply’ button
5. ‘Processing…’ buttton appears and stays indefinitely – THE MODAL DOES NOT CLOSE
6. Click background overlay (or click the ‘Cancel’ button)
7. Refresh the page – image has been uploaded
Media library uploads with out a problem – I have NO OTHER PLUGIN installed and using standard TWENTY NINETEEN theme…