At my peril I'll weigh in. I run a number of workshops. It's just about impossible to have the latest gear from multiple manufacturers or to be familiar with the specific camera settings without working for a camera store. And the cost of mastering different cameras would be prohibitive.
I do agree it is helpful for the instructor to be familiar with both Nikon and Canon gear, the general features and settings, and the limitations. For example, the Canon system offers a histogram with Live View that really helps to nail the exposure in difficult situations.
The good news is most of the capabilities are similar. Both Canon and Nikon use the same technologies for AF. The ability to choose camera settings is similar on both Nikon and Canon cameras - just different locations of the buttons. It's pretty easy for me to talk about a setting and know that it does exist on most current cameras.
If I know that a certain group of settings is going to be used extensively - I want to know how to guide photographers in that area. For example, I frequently follow other forums which are not Nikon specific just to understand the pros and cons of Canon and Sony gear, and how users respond to questions.
The same thing is true for software and post processing. Lightroom is a basic program used by a lot of people. Photoshop is also commonly used. But the most important thing is to be able to describe the strategy for processing or editing. Many of the photographers I see are unsure of their real objective for an image and the strategies that can be used. If we can talk clearly about the approach to an image, the specific steps are going to be relatively easy.
And tripod and ballheads are always an issue. I've had two workshops where ballheads malfunctioned. One had a ballhead lock up and the other had a ballhead stop holding firmly. It's a near disaster if someone has proprietary plates rather than Arca Swiss. If they have Arca Swiss plates, I can loan them a tripod head or even a tripod. I don't want someone's workshop experience to end because of a gear failure.