I think that they should because GOG stands for old school gamers and gaming and 2005 was
11 years ago! I think GOG should support those abandoned people from Nostalrius. It would be good for their PR.

GOG doesn't do MMOs. I'm not sure how they could support those people.

I mean more by making an opinion, that way Blizzard could see, other people in the business don't approve of their actions.

When has Blizzard cared about opinions?

This.

Only when Opinions = Severe Profit Loss will they give a shit.

Why should GoG take action becasue of a privat sever closing?

Don't get me wrong on this, but I expect from GoG to use there "power" to make Cyber 2077 a nice and enjoyable game.

Like The Witcher 3 is.

And it's more interesting to know why the new Starpoint Gemini game (and Dex) is not available on GoG.

It's none of GOG's business, and taking a stance against Blizzard would probably just hurt whatever relation they may have with them and potentially other developers/publishers. Siding with people who were committing copyright infringement could look bad for GOG, especially when the main reason a lot of companies hesitate or refuse to release games here is because they're afraid of piracy.

While I don't necessarily agree with what Blizzard did, they're fully within their rights to have the server taken down.