Right, but the argument isn't that the characters are objectivist, it's that the movie is.
The thing with Syndrome is that the movie doesn't make him wanting to be a superhero a problem because he's bad at it or doing it for the wrong reasons, they do it because he's not superpowered. He seems genuinely keen on helping when he first shows up, in fact. He is just bad at it because his artifical replacements aren't as good at getting it done as natural ability.
Had the movie shown him to have superpowers then the read wouldn't hold, because it'd be his incompetence or his desire for fame and glory that makes him unsuitable, not his inherent characteristics.
But that's not the case. The family's kids are shown as being perfectly fine getting into superheroics. Unlike Syndrome, despite having no gear and never having practiced it much they are naturally talented at it. They're good at it and it's good for them. It helps them feel accomplished and get over their plain-normie anxieties because it's what they're meant to do.
You CAN make a non-objectivist take on The Incredibles and that's called The Fantastic Four. It's the version where the powers are the result of an accident, not a birthright, the non-powered bad guy is a monarch, who HAS a birthright but also a dictatorial position. Where the powers aren't always a self-realizing blessing and can be a curse and the leader can feel guilty for having forced them onto his family instead and vow to work to make them optional. And where the people with powers may be infatuated with each other, but also sometimes with a disabled artist because it's not about the powers or inherent characteristics.
Obviously Bird doesn't think his objectivism or exceptionalism or whatever you want to call it is an immoral or unethical stance. Obviously he thinks the full expression of your talent and the fame and fortune that should come with it are a result of you using your natural talent to help others and lift society up, normies included. Doesn't mean it's not saying what it's saying, though.