Is there any problem I should watch out for in running the Nix package manager alongside Homebrew?

I'm starting on a fresh macOS install and so far only have Nix installed. Can Homebrew coexist well with it or do I have to pick one and stick with it?

My experience so far is that yes, you can run both. I also naïvely installed nix thinking I would use that instead of homebrew, but I soon ran into packages that were only found in homebrew. So I installed both and never had any conflicts. And there should be none, as they simply overlay scopes sequentially. If you evaluate nix after homebrew in your path, it will take precedence, and vice-versa. Their stores are completely separate.

However if you want to be super clean, you can do this:

$ <install homebrew>
$ brew tap caskroom/cask
$ brew cask install nix

Yes, nix is currently just another package within cask! Isn't that amazing?