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"Anyone who supports capitalism isn't really vegan."
They create demands veganism does not make and push away people who might join, without helping a single animal.
Why it is weak
It is the same mistake as demanding that vegans be anti-capitalist, in the opposite direction: it turns an economic position into a condition for defending animals.
There are vegans of many political positions. Economic systems and political currents may be better or worse for animals, and that is worth discussing with evidence, but not by expelling those who came to veganism by another route.
People from different currents can become vegan and later revise their views in other areas. Shutting them out at the door closes that path.
How to say it better
Defend your economic position with its own arguments. For veganism, the question is whether the person has stopped exploiting animals; the rest is a conversation that can come later, and is worth having.
This doesn't mean every strategy, intervention and current is equally good for animals. There may well be a better path, and it should be sought in the evidence: what makes people consider animals, how to save more animals and which interventions work best. The evidence may favor one side. That doesn't stop people from different currents becoming vegan and then revising their moral and political views in other areas, seeking an even greater overall impact.