Don't be scared, it's the same permissions you automatically give to all the extensions on your desktop browser. Apple, however, decided it will be good to scare users away with these dialogs. We never track, collect, or sell any of your data. In fact, Mate is one of the most privacy-conscious apps on the market.
So Mate doesn't stop working after one day.
Without these, Mate can't insert its translation scripts to pages, which are necessary for the full-page translation and Select to Translate.