Is there a place I can set an age so I stop getting popups when I look at FPS games asking if I'm a child?


*The hover over popups are also a nuisance.

At present no. But if they did, they could also hide the adult/eroge games that have been added in recent years too.

But that would make too much sense....

The former would require GOG to actually comply with age identification laws across Europe, which requires a technical solution that they can't just go find an open source implementation on github somewhere.</s>

As to the latter, if not for a recent thread, I wouldn't know that they'd even introduced such a feature.
If you're asking if this is available on Chromium browsers, I'm going to shrug in your general direction and suggest you stick to Firefox.

The "are you 18" popup is not a European thing, in Europe such a disclaimer has no legal relevance.
As you pointed out they don't support verified identification, certain games in certain countries must not be advertised at all.

Both GOG and Valve don't comply to the laws, but when it comes to violent games, no one seems to care. It IS allowed to store the birthdate of the owner, they just don't do it, that's all.
This is a decision, not because they were forced to somthing.

I like those. They allow me to quickly preview and wish list a game without opening the game page.

I don't see any popups, probably because of my popup blocker. The cycling images in the hover popup are hidden for some games however, except the title pic (Lust Element being an example), to view them, I have to click the game page.
I don't know if the ESRB rating is the deciding factor for the images to be blurred out or something else, but I think it's a ok solution for people who don't want to see stuff meant for an adult audience.