Sending out a tweet when a podcast starts live streaming or when a new episode is posted makes sense. It helps a lot of people noticing. But telling the listeners of the show that the best way to contact the hosts is via Twitter seems less true. e-mail, a Slack channel or subreddit would work just as well.
I think that especially if a more or less recurring segment on a show is complaining about how twitter is a toxic hell stew that more or less enabled Donald Trump, a person that the hosts paints out to be more or less Lucifer himself, to get elected as POTUS then the hosts really, really should reconsider whether they want to funnel more communication through twitter and thereby helping the service continue on.