For mostly unknown reasons I want to delete my Google account at some point in the future. The Google services that I am regularly using are Search, Maps, and - increasingly - YouTube. The latter is the only service that really benefits from an account that remembers subscriptions, lists and the history of watched videos.
What I will continue to use are RSS readers. And it turns out that you can (still) subscribe to YouTube channels via their RSS feeds. Reddit is your friend and provides the answers:
The URL for a channel's RSS feed is
https://www.youtube.com/feeds/videos.xml?channel_id= + channel_id
where the channel ID can be found in the html source of the channel page or may even be part of the channel URL. In any case, I now subscribe to my YouTube channels via boring, old RSS feeds.
Update 2020-10-15: My very good friend Zeitschlag tells me that for those channels that do not have set a custom URL, it's enough to just use the channel URL.
For example, Fat Freddy's Drop - the world's very best band btw. - has the channel URL
https://www.youtube.com/channel/UCsLGIbOjsV8TFTco9cL6HHA. Those random characters at the end is the channel ID. When I add this URL to my FreshRSS instance, it finds the RSS feed no problem.
In the case of the hip, young, cool YouTubers like Armen Hammer at
https://www.youtube.com/c/ArmenHammerTV, the channel URL doesn't include this ID but a custom name/slug/identifier. Here, you'll have to go the tedious way as described above.