The problem with taking an approach that aims to absolutely avoid gender stereotyping is surely you'll just be pushing your child into some other social construct. People will find a way to pigeon-hole whether we like it or not (this point I think takes me back to your point about doing things that elicit a response that is favourable to yourself at least).
But I don't think it's necessarily automatic to draw inferences. I find with myself that quite often I miss key bits of information, such as not noticing the clothes somewhere is wearing or if they've gotten a new haircut. I think partly that's to do with not being very observant, but also those type of things don't register highly on my list of priorities. I'd assume therefore that not everyone is necessarily going to notice what clothes your child is wearing or even think about it. If that's the case then maybe they'd just react to the child purely in the way that reflects how they feel towards children in general anyway, such as aloof if they're not a child person, or maybe bubbling with excitement and soppiness if they think children are amazing.
Even if we do automatically make inferences though we can still remind ourselves that they may not be correct, and just ignore the responses that other people give to our child if we don't feel they're favourable?