For what it's worth, those are also hallmarks of crankery. A creationist will happily express ideas, ask questions, and demand proof of claims until the Second Coming. An anti-vaxxer will argue for more research and more caution and advocate for what they themselves regard as objective standards before letting their children be vaccinated - and all the time be effectively telling people that it's better to be dead than autistic. Supporting them for their apparent scientific interests is merely supporting their message. A homeopath has an entire field of professional associations, licensing, and regulation to point to.

What determines whether you're advocating for scientific inquiry is whether you're arguing in good faith for positions that are in genuine need of inquiry, not whether you have the trappings of scientific research.