Unrated players are considered to have a 1200 rating in their first rated game. If your rating didn't change after a win, it was probably an unrated game.
Why does my rating go down when I loose to an unrated player?

Unrated player have elo 1200 so they are not really unrated.
Plaiing with an unrated player will make you gain/lose points. If you are rated much more than 1200 then you will gain almost nothing for win and lose much if you lose, but this is exacly as against anyone else.
I think you are confusing "unrated player" with "unrated matches". If you dont want to affect your ELO you should play unrated games.

Your thinking that 1200 is the rating of an unrated player is incorrect.
Click on any unrated persons name and if they are new no rating will show for them. If they have played awhile there will be a rating next to their name even though they have selected to play as an unrated player.

"USCF used to give new players "provisional" ratings until their rating was established, but even that would not be published until at least four games were rated."
They don't anymore?

The next time you play an unrated player first click on there name.
If they have completed any games before you will see there rating even though the game is unrated. I have seen unrated games where the player had previous games rated at over 1600.
How do you explain that?

Here is a better example of an unrated game:
The above unrated game and the player actually has a rating of over 1400, see below

You are confusing unrated player with unrated game. Just because a rating is displayed beside someone's name somewhere on the site doesn't mean they have a rating for the particular type of game you are playing them in. They might have a 1400 rating in correspondence chess and be unrated in live blitz, for example.

In my opinion win or loose in an unrated game should not affect ones rating, or there should be no unrated games.

I looked into it, and yes, the player you are referencing is rated 1400 in live blitz, as you've shown in your bottom picture, but is unrated in "online chess" which is what you are playing in your top picture.

In my opinion a rating is a rating regardless of where it came from.
In any case, my rating dropped when I lost an unrated game and in my opinion that shouldn't happen.

Presort wrote:
In my opinion win or loose in an unrated game should not affect ones rating, or there should be no unrated games.
I agree. My online rating dropped after playing an unrated game with a friend once. I set up the game and made it unrated. You are not alone. 😊
I think it's happened to other people too. It didn't really matter to me to lose those points but I did find it surprising.
Why does my rating go down when I loose to an unrated player?
My rating does not go up when I win playing an unrated player.