I can't seem to find a solid answer in the forums but can people who bought no man's sky on GOG play with people who bought it on steam, or is there no cross play whatsoever because that would suck.

I think that the answer is "yes." See this announcement.

If you enable multiplayer and visit the Anomaly or the weekend event planet / system then you're pretty much guaranteed to run into other players on other platforms.

After reading the annoucment, it's not really clear about it, but I do believe I should be able to play with users on the Steam version

I have played with Steamers and other gamers. There is also an in-game 'friends code' that makes it easier to connect with players on other platforms.

EDIT: However, there have been reports that voice chat doesn't (or didn't?) always work on the GoG version. I can't say anything about that, since I've never tried it.

Thanks for the information!