This is not simply false, this is the typical FUD spread by people who have no idea how guilds or unions actually work.
SAG does not prohibit non-union actors in SAG-covered productions. In fact, appearing in a SAG-covered production is how one qualifies for membership into SAG.
SAG sets minimum thresholds for pay, benefits, and rights. Actors are free to negotiate better packages if they have the leverage for it. Most don't, which is why the actor-waiter meme is a thing for people hoping to get cast into a SAG-covered role. As someone who has appeared as a background actor in a SAG-covered production: SAG minimums are significantly higher than non-SAG pay, at every level.