I'm personally a generalist in the web and data science areas, but I do specialised consulting under a number of different "personas": Django web development, geospatial data analysis, non-deep data science, SaaS MVP backend web dev, etc.
For each specialisation I have a different resume and "tell me a bit about yourself" pitch, often referring to the same projects but highlighting different aspects of my skills.
When someone says they need a specialist they just want someone who can get their stuff done. Having additional skills isn't a detriment as long as you can do the work, just no need to bring them up in your application.
I always thought that eventually I'd settle into a specialisation as I mastered narrow niches and got referrals within a specialisation. But that hasn't naturally happened, and I'm very happy as a generalist working specialised roles in a wide range of domains.