It is absolutely possible to legally use React while going ahead and suing Facebook. You do not lose your license to React by suing Facebook.
What you do lose is an explicit grant of additional patent rights - the grant given in the PATENTS file. Note that there is no specification therein regarding what patents might be covered; it's completely possible that none of Facebook's patents have anything to do with React. I haven't looked. in any case, patents are totally distinct from you license to use React.
Only if it's possible to use React without infringing (or licensing) any Facebook patents. "Use" is not just about copyright.
(Which, as you point out, is plausible; there's just no reason to believe it's guaranteed to be true.)
Would it be practically advisable to do so?
You have to differentiate between copyright and patents.
From the perspective of copyright you're perfectly in the clear, the grant of rights that's part of the BSD license will not be revoked.
What will be revoked is the right to Facebook's patents insofar they apply to React.js. First of all that that requires, that Facebook actually has patents that apply to React.js. It also means you're no worse off than without a patent grant.
I prefer the Apache 2.0 wording, but this seems to be blown widely out of proportion.
No, see discussion above re: implicit and explicit patent grants. You don't fall back to an implicit grant when an explicit one is revoked.