Knowing C doesn't mean you can't learn React, but if you've only ever done C and low level systems programming means you have a lot to learn to get to the level of someone who has specialized in knowing React and it's environment. It's not just React. It's everything around it that also matters. Such as browsers, HTML, CSS, and all the best practices there. And while I'm sure anyone can learn that, the question is, would you do it in reverse?
Would you hire someone who knew React, CSS, HTML, and web development to write systems level C and expect them to learn it all, and, most importantly, be effective in their role?
Labelling yourself as a react engineer isn't limiting. It's just one of many things. You can have many labels, and adding a label doesn't take away from other things you can do. However, it is an effective way to communicate what skill sets you have to people that would be good to work for and with.