They may block IP addresses associated with consumer ISPs. Assuming that’s the case, I would guess you’re seeing that as an HSTS/TLS error because their network is trying to trick your browser into redirecting to/displaying an error page hosted by some part of their network.
This is just a guess, but I’d imagine that happens because the websites use JavaScript to load the actual content of the page, but Lemmy is just parsing the HTML that is returned.
Also, I really doubt you’d have much luck convincing website authors to completely change their architecture just to get previews to work on Lemmy.