I'd recommend you do. If they get flooded with people reporting the same problem, it's more likely to get a solution

Here is the answer from support:

"Thank you for reporting these issues and a potential fix for one, we have informed our Product Team and they are investigating.
Unfortunately currently we do not have a fix or a workaround.
Sorry for the inconvenience."

I guess we'll have to wait now.

Fairly big problem affecting everyone... did GOG QA this at all? ><

Probably not.

Yup, same problem here. I find it very unfortunate that this sort of thing can happen. Nobody's perfect and everyone makes mistakes but it seems like it would be pretty easy to test if keybindings work before releasing your game.

Could not agree any more. Working of rebinding keys is a crucial test on every PC game.

These are the people that made Descent: FreeSpace they can do it they will fix it for us!

(It honestly doesn't seem like something that would require a major fix)

Maybe they did, saw it worked and moved on to the next test not expecting to loose the keybinds on leaving the game. Or they combined the test with graphical settings, saw the graphic settings work on restart, assumed both share the same file and then moved on to something else.

Strangely, some people report the issue affecting Gat out of Hell as well, while for me saving the control and gameplay settings in that one worked right away.

So who knows, maybe not every installation of SR4 is affected.

So far I only saw ONE person posting a problem with Gat Out Of Hell - might be wrong here though.
But let's test your theory. Anybody here who is able to save i.e. the settings to invert flight?

Gat Out of Hell is a weird one. It saves some setting to the save folder but saves others to what I assume is an unusual location (Don't have Steam version to test). So some things like key bindings save okay but Film Grain does not.

I have tested this as well and it also seems to use two save files. One being display.ini and the other srgDEF_PROFILE. I haven not specifically tried to save film grain but I will test this too. I am pretty sure that the "unusual" location on steam you are talking about is simply the cloud save folder steam is using. At least the srgDEF_PROFILE file in the GOG version is saved inside the game directory but I don't know if this file is storing film grain as well - yet.

Edit: Just reinstalled it to test but where can I even find the option to turn film grain on or off?

Afaik there's no film grain in Gat out of Hell. Only in SR4

Then it is hard to test if what "tremere110" is saying applies here.

Well in SR4 film grain is part of the gameplay options, and the gameplay options in GooH save just fine on my end. They're probably saved in the same file as the user-defined keybindings so my guess is if one works, the other does too.