Private forums that are Auto-Join are readily viewed by everyone. For example, I didn't need anyone's approval to join the Parshuram private forum.
If a private forum is set to Invite Only, it might be because the public forum for the same show has too many fan wars, and members want to be able to comment on fictional characters' actions and personalities without getting a WL increase, and not have to read attacks on real people who work hard to create the show.
If the private forum you want to read is set to Request Join, you can send a request, and maybe follow up with a PM to the Creator/Manager or someone who is a member. For example, a couple of members got into the Ramayana Katha private forum by PM'ing me, even though I couldn't let them in myself.
If you can't get into a private forum, and can't find a public forum, you can go to the Forums main page, click More Shows under the channel where the show airs (or aired), and click the Chat button to get to the channel's Discussion page where you can start a new topic.
From the channel's More Shows page, you can browse the Off Air and Archived tabs to find members who used to post about the show you want to discuss. You can tag them on your new topic.
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