I also tried a Client Side Reader and got into the same issue: CORS blocks requests for other websites.

I now build my personalized feed as a part of this blog’s build process

The author got it working at https://matklad.github.io/blogroll.html; and mark the most important one on https://matklad.github.io/links.html

It is kept simple.

Having a public blogroll also means the followed blogs get page rank back!

Instead of an OPML file, the author use a list of links. https://github.com/matklad/matklad.github.io/blob/ea7bc5161d7b2bc12a7a004408caaefb509b9f92/content/blogroll.txt

The code used is a snippet.