I haven't seen any proof that GOG wouldn't care. In fact I am quite certain that GOG does care, as it can affect their business. How, in your eyes, should GOG show that they care?

For instance, Breach & Clear: DEADline recently got a massive update to the GOG version (the Rebirth update), at the same time as the Steam version. Before that the GOG version seemed to be abandoned for almost a year, no updates whatsoever (IIRC).

Same with Hands of Fate earlier, it also eventually got the updates and missing DLC that were long overdue.

How do you know these were not achieved by GOG demanding the developers to support their GOG versions, after GOG found out there were missing updates/DLCs?

I think the main issue for GOG is to even notice the GOG version is missing some update, this is where the GOG community seems to help them. I am pretty sure GOG doesn't have some person daily checking out games on other competing stores when they get updates and whether they should come to GOG too. I guess GOG expects the developers to send the updates also for GOG, but if they find out some are missing (e.g. due to the active GOG community), then they get in contact with said developers.

Also, lately GOG seems to have started officially announcing of bigger updates for certain games, to me that is also a sign that they do care.