Opponent repeatedly offering draws early in the game?

I’m pretty new to playing anyone other than friends and bots, but wanted to try my hand at a rapid game (60 min). I am not highly rated, and neither was my opponent, 700-800ish. No one was down any material. Tactically, the analysis says my opponent was more accurate, but as I said it was early in the game and I don’t think I was necessarily playing poorly. They kept offering me a draw repeatedly after every move. I just wanted to play, and it was getting really distracting. Eventually they just abandoned the game. Is this typical? Is this something people do when they realize they are playing someone that isn’t as skilled and they just don’t want to waste their time anymore?

...They probably had to leave and didn't want to lose rating.

Normally, people do this when they're sore losers and have just blundered their queen.

Even if that's not the case, there's no excuse to do a long game if you can't stay for a long time. I get that things sometimes pop up out of nowhere, but that's why you should be prepared. If you have even the slightest suspicion that something might happen, don't do a long time control.

Ok, so what is the etiquette here? Should I just take the draw if they keep offering? Does accepting a draw under those circumstances affect my rating? I wouldn’t care that much about my rating except I want to make sure I am matched with reasonably similarly skilled opponents.

There is no etiquette, it’s ok to keep playing the game. Personally if something crops up I resign the game as I would if it was face to face, I wouldn’t keep hassling for a draw in real life and I don’t appreciate it happening to me on line.