Do people really think Facebook developed and released React for the sole, or even primary purpose of gaining patent rights? It's preposterous that so many top engineers would be working on such a goal.
It seems obvious that Facebook just has some overly cautious lawyers. I highly doubt that means Facebook is going to use your usage of React as an excuse to steal your patents.
Having met with their legal and open source departments and talked about this before, i can pretty much say "they have a reasonable set of problems, and are trying to do a reasonable set of things about it".
One can argue they don't need to be this harsh about it, etc. But that's about risk tolerance, not about trying to gain more rights.
It's not like React is a massive library with a huge surface area. Even a fairly complex application could be migrated to an alternative like Vue.js if the need arose.
Or a non-issue if you choose a framework that you feel has safer licensing.