Also using AntennaPod from F-Droid here: it gets its data from CDNs. The CDN is in a position to log data from a lot of people, that's why I think they are on the block list.

It depends on which podcasts you listen to which services you need to unblock I think. The 'essential' category is usually a good starting point but you might need more, especially for the search which iirc comes from Apple/iTunes.

You can also just whitelist AntennaPod completely of course, being an open source app from F-Droid that's relatively trustworthy.