That's not a good idea, because that would allow any website a logged in user visits to impersonate them (e.g. link to a malicious site posted somewhere, users click on it, JS on the site starts posting the same link in their name, more users click on it, ...).
But react native doesn't restrict cross-domain access like browsers do, so it shouldn't be an issue in your case: https://reactnative.dev/docs/network#using-other-networking-libraries