What material can I use to insulate NFC tags so they can be placed almost back to back?
I think there are two possible solutions for back-to-back posters with NFC tags:

You can buy special NFC tags that are for use on metal surfaces. (They have a built-in metal backing a short distance behind the NFC antenna, and everything is tuned to work with that gap. So they work on both metal and non-metal.) They do have a shorter range and are a bit more expensive, like $1 apiece. With those you could put foil between the two posters and have no worries.

As commenters suggested, if your posters are wide enough you could do something like put the tag on the right side of each poster, so the tags are not back-to-back. This is error-prone if users wave their phones all around the poster though. (And, your solution of adding a gap between the posters also works.)