This is not true. The Red Cross in my country, which is an ICRC affiliate, does provide disaster relief. As far as I can tell, this is true across the board.
Eg:
https://www.redcross.org.au/news-and-media/news/australian-b...
https://reliefweb.int/report/viet-nam/thai-red-cross-society...
For disaster relief you'll have to find another reputable charity.