Hey @sergei, @RomanStoffel
I have good news - I reported a defect to Firefox yesterday and they responded with some useful hint:
They claim that the problem might be caused by a stetting fission.autostart that for some already existing profiles is set to true. When you create a new profile, the value is automatically set to false and that’s why links are clickable within new Firefox profiles.
I’ve tried changing it to false through about:config tab on my existing Firefox profile and it worked like a charm. We did the same thing on my colleague’s Firefox that faces the links problem, fix also helped 
More details here:
We will wait for Firefox to respond before informing users about this workaround.
Could you try it out if it helped for you if you’re facing the issue as well?
Best regards,
Alicja