I'm showing my age, but back when IE was basically the only browser and Firefox (Firebird back then) launched, people often lamented that things didn't work in Firefox. The solution? People used Firefox and web developers were forced to make their shit work in Firefox. When Chrome came out, suddenly we had three real options and the way to make everything work? Open Standards.

Now, Chrome is in the position IE was back before Firefox came around. How ever will we make sure things work in Firefox??? Use Firefox. If enough people dump Google's malware browser, the web has to go back to supporting multiple browsers through open standards.

Have you reported issues for them? It's in the menu somewhere. If Mozilla get a lot of reports for particular sites, they reach out to the webmaster and try to work with them to improve Firefox support - usually by removing proprietary Chrome-only features or by removing reliance on Chrome bugs that don't exist in Firefox.

You can also report the issue at https://webcompat.com/, just search to see if it's already been reported first.

Same. For me, the big one's my bank that requires its users to use Chrome, else it won't let you log in. I got around this by using an agent-switcher extension in Firefox.

Which sites?

User agent switcher. I have zero issues since using it.