Really depends on which extension you actually install. For example using something like ClearURLs has no way of impacting your fingerprint. Telling people that they can’t install extensions in general is deceiving, instead you should just suggest to consider the pros and cons of each one specifying that some are counterproductive.

For the second part, Bromite is great and I’ve been using it for quite some time, but you have to be aware that using a chromium-based alternative still indirectly depends on google. Using firefox or firefox-based alternatives is the best option