Cavalary: *blink* Why would it be unsafe? And didn't you do so in order to post here? Do you not log on anywhere else from browsers? E-mail, social networks, stores...?
(Of course, I would never touch Galaxy or clients in general and their very existence on a system looks potentially unsafe to me.)
I'm here from the launcher. I go to a game from the store, click on the forum of the game, and than go to the community from there. Over a decade ago I watched a YouTube video where a guy was talking about Steam, and he said that it's safer to login from the launcher just in case. Since than it just become natural to me to always login from launchers when it comes to video games.
Palestine: Are you paranoid for a specific reason, or, is there a general fear that the browser (or, the GOG web site itself) is somehow tainted?
For (nearly) 13 years, I have been logging into GOG via various internet browsers (and had only briefly tried the GOG Galaxy client in 2015), with no issues whatsoever.
I just think that it's easier to hack an account if you login from the launcher. I might be completely wrong but it's like an OCD I guess.