Wanted to thank everyone for their suggestions. Lots of good information here and more to choose from than I had expected.
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I use Newsify. I looked at several RSS readers and liked this the best. I pay a small subscription to use their syncing, but you can use iCloud for free. The subscription also provides other benefits like automatic full text dowlnoads. Both Mac and mobile apps are available in the app stores, but oddly there’s no link to the Mac app store on their web page; find it by searching.