I've been trying to pay for an order for several days now, but every time I bump into the same problem as before - some payment methods don't load at all (in this case, blanks for credit card details don't show up). I've seen posts about similar problems, but none of the suggested solutions (like trying a different browser/device, allowing all cookies or turning off any antivirus software or browser extensions) had worked for me.

Do you have any ideas how to resolve this?

It seems like you said you tried a different device/computer. So this may be unlikely, is there any chance you are blocking scripts from any of these three domains at the router?
checkoutshopper-live.adyen.com , live.adyen.com , pay.google.com

Scripts from all three domain are required to load the credit/debit card info form since about november 25th of last year.

Have you try to use your phone? Have you tried use paypal or other methods? I just purchase a game an hour ago and was working fine, I don't know what could be... :/

Hello TheSaltyGaben!
During the latter half of the past year, I had the same problem. My usual browser stopped loading the payment process form for credit cards. At first, nothing seemed to solve this issue (private browsing tabs, deleting cookies, enabling or disabling the various third party functionalities, etc.). I even tried and started to use Google's Chrome browser, without success.
Later, I tried several recent but not most up-to-date versions of Firefox and different forks until I found one that worked for me. Upon updating to the most current version of it, the payment process stopped working again.
So, I downgraded it back to the (for me) working version, which I am keeping and using only for this purpose--a quick login in order to complete the buying process here on GOG.com.

I hope you find a working solution for you!
If not, contact the customer support from GOG.com and do not forget to choose the "Orders & Payments - Problems with completing a payment" option.

I know, it can be quite frustrating to miss certain offers or sales periods here due to such an error.
Good luck!

Kind regards,
foxgog

Thank you all for your answers! I've read them and they gave me an idea. I've dug a bit deeper and searched through the page code. Turns out, every time I want to use the credit card, it gives a certain error. Basically, it wants an 'Access-Control-Allow-Origin' header so the CORS policy won't block the request. That's where the things get complicated for me, since I'm not so good with coding. All I've managed to come up with is to use extensions for Chrome to make the script work but unfortunately it doesn't. Any further suggestions would be highly appreciated!

api.rollbar is not required for credit card form to work.

Since it looks like your are willing to dig a little, I suggest you go the network tab of the developers tools. With that tab showing in the developers tools, click in the web page area to make sure it has focus and press <control+shift+R> to do a forced reload of the web page. You should see detailed information about all page resources. If you don't see the "domain" section like in my screen shot, you have to right click on one of the headers "name", "status", "type", "initiator" and choose what section you would like to add from the pop up list.

Thanks for the heads up, done. Got these as a result, and GOG keeps insisting that there's something with CORS every time I select this method. Thought that the reason might be behind pay.google.com, but so far I hadn't found a similar case.

That 403 error on the pay.js for pay.google.com is your problem. A html 403 error is resource forbidden though. That suggest that the pay.google.com server refused access to the script rather than pay.google.com being blocked by something. That pay.js script is required to load the credit card info form.

Here is a direct link to the script. Try accessing just this script by pasting the link in a web browser address bar.

https://pay.google.com/gp/p/js/pay.js

If you still get a 403 error with the direct link, the only things I can think of are that pay.google.com black listed your ip address(maybe you are using a vpn that got black listed) or you are running some type of internet security/anti-virus software that is trying to "protect you" from the script.

I've had my doubts before, but now I'm almost sure the problem is my ip. Maybe it has to do with my location at a so-called "occupied" territory that is being sanctioned by many companies on the internet. Though it seems weird to me that vpn does not help at all. If it's the latter case, I have no idea what could be blocking it, since I've already allowed JavaScript for almost every site related to this problem, even had all my extensions and Windows Defender turned off.
Well, I can only hope it's a false positive fraud case like those I've seen mentioned before and GOG Support can do anything about it. But anyways, big thanks to you, my friend.

Not all VPNs are equal. AND you can be still leaking some traffic outside VPN which would make it even worse than not using it.