Do you remember the poll a few years back, about games requiring a third party account for multiplayer? The specific question about Planetary Annihilation? The majority of those that answered said that they wouldn't mind, and it was a third party account, not the GOG account. So I'd say that people wouldn't mind if multiplayer was locked behind Galaxy, though that's just a personal opinion.

I remember that poll. I also remember the poll right before that where they asked roughly the same question about whether it would be ok if they added some sort of key access to multiplayer and it got a resounding 'No' from the people answering it.

Then in that next poll they rephrased it quite more 'benevolently' towards the players with the Planetary Annihilation example, and then it 'passed' positively.

It's all about how you word it, how you spin it.Basically, all they have to do is say it is for the benefit of us, the customers.

"Yes, we are 'forced' to because the 'market has changed' but as a result of that we will be able to offer you more games than we otherwise could have gotten for you ". Or "We will always continue doing our best to deliver you DRM-Free games now and in the future*, however, for the benefit of our customers who enjoy the GOG Galaxy multiplayer features (and coincidentally publishers) it is necessary for us to maintain a certain level of quality to the multiplayer service we offer through Galaxy. But don't worry, your games will remain 100% DRM-Free, using Galaxy is entirely optional! (But yes you will have to use it for multiplayer and you will need to own the game)"

*despite promising the same for fair pricing yet according to some devs their standard offer includes regional pricing now)

It probably varies from person to person. If they hide LAN or do not other such connections as LAN I may not buy the game. If a third party server is available or if the connection to a server seems reasonable I might just treat Galaxy as part of the general game infrastructure. So times I may mind and decide not to buy other times it might be fine.
We could count how many threads there are aboiut how to add friends / why adding friends is really difficult and then we could count how long GOG needs to introduce a feature where you search for a user and then add them within Galaxy. It might take a while. Maybe if PCGamer would write about it...

GOG profiles itselves as a no DRM games site/seller. So GOG should keep in mind to NEVER make Galaxy mandatory and to make Galaxy only a pure voluntary thing especially on a no DRM site as GOG. Also this means that GOG should keep updating the individual GOG game installers for all the GOG customers including those that never will install Galaxy.