Ask what the user is gaining by having to interpret a category by an icon (without text), and also having to interpret each category by a series of colors.
I know your question is about mutual categories, but I'm proposing you simplify your category display, so you can more easily distinguish mutual categories. (I know I don't have the design constraints you may have)
Icons alone are hard to interpret.
If it's information that needs to be read, you could try using text (or at least icon w/ text).
If you do need to use, icons, there are some good guidelines.
From Neilsen Norman - Icon Usability:
A user’s understanding of an icon is based on previous experience. Due to the absence of a standard usage for most icons, text labels are necessary to communicate the meaning and reduce ambiguity.
You could supplement with a label:
To help overcome the ambiguity that almost all icons face, a text label must be present alongside an icon to clarify its meaning in that particular context. (And even if you’re using a standard icon, it’s often safer to include a label, especially if you slightly altered the icon to match your aesthetic preferences or constraints.)
You have two levels of interpretation here (icon and color of category); wondering if it could be simplified.
Do you have a reason to hide meaning behind an icon? And have a color change for each category as well? Is there anywhere else that color in your UI has a meaning, i.e. an indication of system status?
Here's a version w/ text only, similar to how linkedin looks at skills as lozenges.
Since I don't have clarity about how many categories you have, here's a simple version, and another with the icon and text. I admit I don't know the role that categories play in other parts of your app.
download bmml source – Wireframes created with Balsamiq Mockups