I am looking for an integrated system featuring an open source Linux client that streams music and radio stations that are published under a free license.
So basically a truly FOSS alternative to Spotify and others. If such an ecosystem exists, then I would like to support it through donations.
Short answer: No.
In the FreeGameDevWiki you can find an up-to-date list of web services of FOSS music (CC:BY and CC:BY-SA).
Of those, the only one I am familiar with is Jamendo, and while it does offer something called “radios”, I do not think that you can exclude non-FOSS music from them (all music is CC, but CC:BY and CC:BY-SA are definitely not the only licenses used).
By the way, although the UI suggest that you can only search music with a certain license, you can use the following Jamendo URL to browse both CC:BY and CC:BY-SA at the same time: https://www.jamendo.com/en/search?qs=fq=license_cc:%28-nd%20AND%20-nc%29
I suggest that you download whatever you like and play it locally.
About donations, check the remaining sites. I would certainly discourage you from donating to Jamendo, as they are basically using FOSS because they saw an opportunity there, they do not seem to care much about the FOSS philosophy.
I don't know (2018-06). But I heard about someone who got hold of TotalRecorder (other FOSS alternatives for Linux / Windoze may exist for all I know) and found that she could capture any streaming audio input and turn it into MP3 files.
And this same person then used a FOSS app (e.g. Audacity) to edit the resulting MP3s to edit out all the annoying adverts, split albums into recorded tracks. Just a thought...
Then again, you could always choose to pay Apple Corporation lots of money, about 95% of which (allegedly) doesn't go the artists: freedom of choice, the 21st Century way!
