Sublime 3200 integrates Git in the gutter, but in a way that ia a little too visible in my taste.
https://www.sublimetext.com/docs/3/color_schemes.html#global_settings-gutter
To make it less visible I modified the different .tmTheme files I use and added:
<key>line_diff_width</key>
<string>1</string>
<key>line_diff_added</key>
<string>rgba(118, 255, 118, 0.5)</string>
<key>line_diff_modified</key>
<string>rgba(255, 195, 128, 0.5)</string>
<key>line_diff_deleted</key>
<string>rgba(255, 118, 118, 0.5)</string>