The full error message is
This Version of Lightroom may require the Photoshop Camera Raw Plug-in version 9.10 for full compatibility.
Lightroom: 2015.10 Camera Raw 9.10
Camera Raw (in PS) 184.108.40.2069
So how do I get Lightroom to recognize the correct version of Adobe Camera Raw?
I have this same problem—all my apps are the same versions as yours. The only difference is that I am operating MacOS 10.11.6.
I was about to post this when I saw your questions—thanks.
It's a known, benign bug.
Adobe is working on it and will fix it in the next update. In the meantime click "Open Anyway" and all will be well.