This appears to be a related issue only on iOS: since updating React Native from 0.55 to 0.57. adding credentials: 'include' helps, but this flag does not help if you reopen the app. Cookie will be deleted after app relaunch.
Below link actually proposes a PR release around this, but even that is not resolving the error. https://github.com/facebook/react-native/commit/a6860487947ae0957f5dfa4979e92bc7740fecb0
This is addition to the file react-native/Libraries/Network/RCTHTTPRequestHandler.mm
- (void)URLSession:(NSURLSession *)session
task:(NSURLSessionTask *)task
willPerformHTTPRedirection:(NSHTTPURLResponse *)response
newRequest:(NSURLRequest *)request
completionHandler:(void (^)(NSURLRequest *))completionHandler
{
// Add the cookies to the new request
// This is necessary because we're not letting iOS handle cookies by itself
NSMutableURLRequest *nextRequest = [request mutableCopy];
NSArray<NSHTTPCookie *> *cookies = [[NSHTTPCookieStorage sharedHTTPCookieStorage] cookiesForURL:request.URL];
nextRequest.allHTTPHeaderFields = [NSHTTPCookie requestHeaderFieldsWithCookies:cookies];
completionHandler(nextRequest);
}