Forwarding something false makes you a delivery driver for a lie.

Not writing something does not remove you from what happens to it. False claims need carriers far more than they need authors, since one post reaches almost nobody without a chain of people passing it along in good faith. That chain is where the damage actually gets done, and it is made of ordinary people who meant no harm.

Treat sharing as a statement rather than a relay. If you would not be comfortable defending the claim tomorrow, do not move it today. A short pause between reading and sending is the only tool required.