That's not how it works.
The patents file does not take away any rights or impose any obligations.
You already have a license to use the React software, because it comes with a BSD license.
The patents file is an additional grant of rights. Specifically, the right to immunity against Facebook patents related to React, unless you have yourself initiated a patent lawsuit against Facebook.
The Apache License and the Mozilla Public License also contain patent retaliation clauses. Not many people care about this, and not many people even read licenses or think about what they mean, except in the case of React, because it's become a FUD meme.
Here's from the Apache License, v2, clause 3:
"Subject to the terms and conditions of this License, each Contributor hereby grants to You a perpetual, worldwide, non-exclusive, no-charge, royalty-free, irrevocable (except as stated in this section) patent license to make, have made, use, offer to sell, sell, import, and otherwise transfer the Work, where such license applies only to those patent claims licensable by such Contributor that are necessarily infringed by their Contribution(s) alone or by combination of their Contribution(s) with the Work to which such Contribution(s) was submitted. If You institute patent litigation against any entity (including a cross-claim or counterclaim in a lawsuit) alleging that the Work or a Contribution incorporated within the Work constitutes direct or contributory patent infringement, then any patent licenses granted to You under this License for that Work shall terminate as of the date such litigation is filed."
So if you sue over a patent, the Apache patent grant terminates.
Here's from the Mozilla Public License, v2, clause 5.2:
"If You initiate litigation against any entity by asserting a patent infringement claim (excluding declaratory judgment actions, counter-claims, and cross-claims) alleging that a Contributor Version directly or indirectly infringes any patent, then the rights granted to You by any and all Contributors for the Covered Software under Section 2.1 of this License shall terminate."
This is even stronger: if you sue over a patent, the entire license (not just the patent grant) is terminated, so that you would then be violating copyright law by distributing software based on that MPL project.
Nobody ever mentions that patent retaliation clauses are fairly common in open source, and nobody definitely goes into any detail about what they mean and how they differ.
This issue is a textbook case of FUD (fear, uncertainty, doubt).