If a website doesn’t work in Firefox (due to a bug in Firefox or the website or because the website blocks Firefox), please file a bug report on https://webcompat.com/
Mozilla developers will then try to reach out to the website’s owners, add a fix or workaround in Firefox, or (as a last resort) spoof Chrome’s User-Agent string to bypass the website’s Firefox block.
>>cpeter+(OP)
In some sense, doesn't the existence of that site kind of strongly indicate that the GP's point is correct. That there are spotty incompatibilities?