I see. Is the main site URL stored in the database, too? So it is not a matter of a local instance configuration? In that case it would be clear that both instances would still try to serve the same thing.
And you are right that two-server setup still doesn’t help Discourse to choose the right theme at all.
Now it reminds me that there would be a problem with the content, too. If you paste a link into Discourse, it posts the whole URL into it. So someone reading a topic authored by the other site would be directed to it when clicking on a link. Same with uploads, see Uploads Path Should Update When URL Changes in app.yml During Container Rebuild.
Another problem could be e-mails? From which domain would the notification e-mails go? Another problem – social plugins (Facebook etc.) or Google login would redirect to a wrong site (or maybe refuse the sign-in).