Can't open FILE - "unidentified developer" error?

1) I export a Keynote file to PDF.

2) I double-click the PDF in Finder, and it opens in Preview.

3) in Finder, I "Get Info" and change "Open with" to Acrobat Reader.

4) When I double-click the file, I get "can't be opened because it is from an unidentified developer."

I know I can go into Acrobat Reader and open the file from there. Or I could go to System Prefs>Security>General and "Open Anyway." But I have a large number of PDFs that I need to open in Reader. I don't want to have to do each and every file, one by one.

(And why does Mac OS suddenly think a PDF is an application anyway???)