So, sitting at ~1200 rating, most of the time I would get unrated players when I seek games.

Most of the time, these players are a box of surprise. If they are weak it is fine. But what if they are very strong players just starting out? Then you will most likely lose and since their (current) rating is low, you will lose considerable points. I know, the rating is not that important, but it is what matches you to people of your playing strength and I want it to stay that way.

So TL:DR; how can I exclude these people when seeking games?

Get over yourself.

Thanks but that reply did not help.

You can set the minimum rating and maximum (not less than yours) for your open seeks opponents.

The average rating on this site is pretty close to 1200. So in the long run the rating effect of playing noobs should level out.

If you really want to avoid such games you have to set the rating filter to exclude 1200 (e.g. 800-1199 or 1201-1600).

You won't, because their Glicko RD is very high.