Hello everyone, today I discovered that I have the same problem. This happens for the german podcast “Mit ohne Ahnung”.
A few words towards my infrastructure: The RSS feed is being hosted on https://mitohneahnung.de but the actual file hosting happens on https://backend.tobiasmaasland.de/
So that means at some point a 302 happens from https to http and no certificate is available. As far as I know such a redirect can be disallowed by browsers. Assuming the streaming engine is different from the download engine in Google Podcasts, this might be a clue towards why this is not working.
Also just to add this: I can see in the access.log within mitohneahnung.de that 4 queries against the page are made when I try to stream a podcast. But those are the same 4 queries so I suppose the app is re-trying. See the following row which appears 4 times, also see the 302 redir:
[04/Apr/2019:15:31:44 +0200] "GET /podcast-download/109/5-olympia-1904.mp3 HTTP/1.1" 302 26 "-" "Mozilla/5.0 (-my-device-; wv) AppleWebKit/537.36 (KHTML, like Gecko) Version/4.0 Chrome/71.0.3578.99 Mobile Safari/537.36 GSA/9.46.5.21.arm64" "mitohneahnung.de"
So for everyone who is hosting themselves: Is it possible that your infrastructure has also a mixture of secure / unsecure connections?