Site Identity is fine to use with Kubrick, and actually recommended, as it's the easiest way to get some of the page-top content in place.
If the menu works ok in another theme (and the searchbox), then it would appear to be a theme issue, and could involve padding or other layout specs of the page top (kind of invisible intrusions blocking mouse access to underlying page parts — that sort of thing). But it's hard to say, and impossible to be specific, without actually seeing the site, I think. I checked your domain and got a can't-be-accessed error.
The Kubrick theme does work, as it does on my test sites and others where it's been installed. But the flexibility of configuration and so on can sometimes lead to problems.