Non offensive word for people who are not single-magisterium-Bayes thinkers

I too find your friend's statement uncompelling. There's no reason to limit yourself like that; even assuming that the multiple-intelligence premise is true, the correct solution is to apply 100% of your logical-mathematical and interpersonal abilities. You might want to practice the logical-mathematical part first, to achieve a better ROI, but that's not the same thing as saying you should apply 60% of your ability just because logical-mathematical contributes to 60% of the result.

Unfortunately people usually find it distasteful to apply S2 to things that they're used to using S1 for. I've found that S2 is associated with negative feelings of coldness, calculation, and inauthenticity, so I avoid talking about rationality (when memes like "love isn't rational" dominate, good luck bridging the inferential distance). Instead, I solve their problem myself, and frame the result in their language. Your friend would probably accept advice of the form "do X, don't do Y, here's why [touchy-feely explanation]".

Some examples, just off the top of my head:

• Don't use words like S2, inferential distance, math, utility, pattern, strategy, intelligence, signalling, or efficiency. This is not an exhaustive list
• Don't bring up probabilities, odds, or frequencies.
• In fact, don't mention any numbers. Numbers are an automatic fail unless your friend brings them up first, and even then, be careful not to take that as permission to go full-bore mathematician
• Equations count as numbers. So do theorems, proofs, or anything that even vaguely pattern-matches to mathematics.
• Pretend the words Bayes and rationality are unspeakable curse words
• Any time you feel the urge to say "optimal", say "good" instead
• Don't accuse your friend of being stupid or toolboxing, no matter how dumb or crazy they get
• Replace S1 with gut or heart, and S2 with head.
• Don't talk about near/far... in fact, if you read about it in the Sequences or on LessWrong, you'll probably lose points for talking about it (but you can still use the techniques and skills behind the scenes, just not openly).

Yes, this is hard. It'll get easier as you practice and becomes an S1 process.

Say that listening to someone makes a friend 80% of the time and talking at them makes a friend 20% of that time. 

The kind of mental model you need of friendship to model it in a way where that sentence makes sense might not be conductive to winning friends. 

The problem is that my friends find Toolboxism an offensive descriptor. 

Toolboxism isn't an inherently offensive descriptor. It's however not a term that describes the way of thinking that your friend describes in your quote. It might not be that your friend finds it offensive, but just finds it wrong. 

It's problematic to have a mental model where you expect people to either be blues or greens and not be open for someone to come with a different position. 

The idea of orthogonality isn't part of toolbox thinking the way it was previously described. When David Chapmen transfered what he learned from a religious ritual to his DARPA AI research Chapmen transfered knowledge across domains. 

I believe the term you are looking for is a fox, in the sense of Tetlock. But honestly, as someone who is generally pro-toolboxism, I don't understand why that's offensive. The whole point is that you have a whole toolbox of different approaches