Disclaimer: I've never done this before, but this is what I'd do.
Approach branding in the same way as internationalization. Instead of hardcoding strings, reference a config file that translates the logo/brand names/color scheme for the specific deployment. Look into how Shopify does this for their customers.
yeah something like that is decently easy on web... I think it may be a more significant challenge on the Mobile side. I'm also curious about things like... should we have 1 github repository for the base app and then branches for each customer, or some other type of code management setup.
I haven't done this for mobile but have done for web. I imagine for mobile it becomes part of yout build process? Eg. Your build runs and looks for a config named like the client name, from there you swap out designs.
For Github we had the base app in one repo and client apps in their own repos. This was more out of necessity as we had different clients on different versions of the product / with their own custom functionality.
That's not a good use of branches. A live product shouldn't need to pull in 100 branches.... Just keep it simple, a directory called branding with a subdirectory for each client. Ideally shouldn't be code, just assets and maybe a simple css or color file.
Approach branding in the same way as internationalization. Instead of hardcoding strings, reference a config file that translates the logo/brand names/color scheme for the specific deployment. Look into how Shopify does this for their customers.