The AdSense terms of service prohibit serving ads on pages with content that violate copyright laws. See the section on "Intellectual property abuse." To show ads on content from Instagram, you would need to obtain permission to display that content before you would be able to show ads with it.
In the case of Instagram, Instagram does not claim ownership of the photos on Instagram. The photos are usually owned by the person who took them, although they could have already been sold or owned by the person's employer. This means you would usually need to have the permission of the Instagram user to show the content from their account. Once you have this permission, your showing it would be legal and you would not violate AdSense policy about copyright.
The AdSense ad placement policies prohibit placing advertisements on "content that we cannot evaluate." Google's software for choosing ads for pages requires text content to know what the page is about. If your page has only Instagram images and no text content, Google AdSense won't work because the page can't be evaluated for relevant ads. To apply and get accepted by AdSense, you site needs sufficient content: 50 pages with 300 words each.
Certain images might also violate Google AdSense policies. You would have to police the feeds and make sure the images don't contain prohibited content such as pornography, weapons, drugs, alcohol, or illegal activity.
