This is an issue with the site's RSS feed, not Feedly. Feedly has an option to open any individual feeds posts in an in-app browser directly (and if you're on iOS, even enable Reader mode!) to combat this, so you don't need to switch apps!
I use Reeder for iOS + Feedly. What the OP describes started happening to me with all sites at the same time 2 days ago. Interestingly, it does not happen on the main Feedly site. So I do think that Feedly is making the experience worse with third party readers. I would speculate that this is done because third party readers don’t show ads.