Your end product has both HTML and JS so there's no way around mixing them somehow at some point. You could do it by keeping them separate and linking between them by means of CSS classes and magic strings in HTML templates. Or you can generate the HTML using JS functions. JSX just gives that latter option a pretty syntax.

If you don't like mixing logic into HTML you're free to create dumb components that only contain as much logic as you would want to put in a template. Such a component would accept properties and output a representation of the resulting HTML. A smarter component that does not generate HTML will provide the logic required for the template to function. That approach actually encouraged and is the right way to do React.

The bonus of this whole generate-HTML-representation-with-functions thing is that you pass around native JS values instead of stringified values and magic strings. Want to provide an onClick callback? Pass a callback. Not some magic string that represents a key which holds the callback in some object defined by framework-specific convention. No, you just pass a raw javascript function that will be run on click.

This might seem like a trivial distinction, but it's the difference between writing native JS vs writing magic framework code. I vastly prefer the former.