Are we still able to play with our steam friends if we buy a copy of the game on GoG?

No. Unfortunately there's no 'crossplay' between the GOG and Steam versions.

That's disappointing. I wonder what the reason is. Anti-cheat maybe? Steamworks integration?

I doubt it's anything to do with cheating. There aren't any leader boards or anything like that and you can mod/cheat the Steam version just as easily as the GOG version. It's more likely something to do with issue between the Steam API and GOG's Galaxy API.

More like "already" because if the functionality would be there they wouldn't remove it.
No. It does not seem like they "already" implemented this functionality.
Seems like we still have to wait.

It is definitely not related to any kind of cheat detection.
It is also not very likely for the reason to be steamworks as it by itself is pretty flexible (if network backend even relies on it at all, but I'm not gonna dwelve into more details on that that as you are probably not in gamedev and I don't feel like explaining everything).

The most likely cause is the network backend. Unfortunatelly I personally don't know if it relies on valve network at all in this case. Steam related services have nothing to do with actual online content in game. If a game has online content it may rely on valve servers but it may also use it's own. It is entirely up to developers to decide what they use. I don't know what they used in this case. I may ask around and investigate that (I am somewhat interested in that myself) but don't expect any update on that from me for at least days as I'm busy now and it will take me some time.

Some things to consider:
1.If they don't use valve network just their own then it would mostly be the case of optimising it to work with two different platforms for crossplay to work (at that point they could as well make it possible to play with console people too).
2.If they use valve servers it would somewhat add to complexity but it still would be possible to implement crossplay.
3.Well gog version does seem like lower priority unfortunatelly
4.Store page on gog pretty clearly states " Multiplayer is available only between GOG.com users. " right now.

(Luke)

There is some sharing of the universe between GoG and Steam. It appears that discoveries and bases exist in common pools for all PC players, with separate pools each for PS and XBox. Real-time interactive multiplayer, not yet however.

It's possible, I suppose, that Steam actively discourages cross play between Steam and GoG.

This would indicate that some part of netcode relies on dedicated Hello Games servers while part of netcode related to realtime multiplayer relies on GOG / STEAM servers. It is very highly unlikely. Valve is not epic games. Even if they would try they really can't stop developer from using their own servers (which they are not even trying to stop. Again Valve is not epic games).
Besides there are already some games that have crossplay so this claim is sort of automatically invalid.
What is most likely is that implementing crossplay with GOG cumbersome API (it seems pretty terrible) is taking more effort than Hello Games would like to take on at the moment and thus it is taking them more time than it should. Also perhaps they are not even actively working on it at the moment now, who knows :/

Steam does not allow cross play. However if your copy is from gog & theirs is on steam I've discovered a little work around. If you are both on epic or origin those do qllow cross play. Caveat being that the game you are playing on gog gives you the option in game to use your epic friends list. But I just did this tonight with Dying Light

I've met with a Steam friend while I was playing on GOG before. We just met in game so I'm not sure if that's what you're talking about.

Crossplay has been in the game for quite a while now:

https://www.nomanssky.com/2020/06/introducing-crossplay-for-no-mans-sky/

Yes. Voice chat won't work, you'll both need to use a separate solution for that (Mumble), etc.

I bought this game on GOG and played with a friend of mine who has it on Steam a couple weeks ago. It doesn't just work, it works really well IME.

I play NMS GOG version in Linux and I'd like to play with some friends who are on Steam. Would this still be possible?

Yes, and you can also play with people who have it via Microsoft, Xbox, and Playstation.