Startup – testing – unittesting habits & best practices?

I'm a CTO in a tiny startup, and curious about what others have learned about testing in startups. We've been around for two years and currently there are 3 fulltime developers, including me. Our codebase is < 500 000 lines and it's purely backend written mostly in Java.

Personally I've written unit tests only when developing a complex datastructure or some other (business-)critical part of the system. One developer in our team pays a lot of attention on unit testing, and writes huge amounts of unit tests. I respect his opinion, and I've given him the time to create the tests he thinks is necessary. I just think most of what he is doing is waste of (current) resources, as having bugs in non-business critical parts of the code is not so important, and some of the things he is testing with unit tests, would be a lot quicker to test with basic integration tests before merging code to master. Because he is writing the unit tests, he delivers new features much slower than others.

So I'm curious to hear, from startup CTO's, how have you successfully combined the lack of resources and testing in a startup? Or how has the lack of (unit / other) tests destroyed a startup? Or from developers working in startups, what kind of unit tests are you writing, and how do you feel about it?