I don't think it hurts your SEO–since it's framing your page at the same URL. Google is smart enough to know that the frame comes from your site/blog.
Honestly, I don't think you should be too concerned about it. After all, RSS readers, blog search engines, news search engines, meme aggregators, and other sites all scrape content and republish it (in whole or part) in their own pages–often profiting from ads at the same time. Is that any less shady to you?
I'd say just make sure your pages clearly define you as the content creator. People will get the idea.
In some of those cases, the practice is just as shady. In others, not as much.
I don't use an RSS reader personally and never will. I visit the sites I like so they can recoup advertising views from me reading the stories they paid real money to professionals to write.
I also don't like how RSS readers make every story look the same no matter where it comes from. It loses personality.
I think newspapers are partly in their current situation because they didn't sue the pants off Google or charge for their sites to be spidered 10 years ago, before the public grew comfortable with the practice. Google got all their data for free.
If I'm expected to pay Twitter for use of their API, surely I could have been expected to pay the NYTimes to spider their site and store local copies of all their content.
Honestly, I don't think you should be too concerned about it. After all, RSS readers, blog search engines, news search engines, meme aggregators, and other sites all scrape content and republish it (in whole or part) in their own pages–often profiting from ads at the same time. Is that any less shady to you?
I'd say just make sure your pages clearly define you as the content creator. People will get the idea.