Umm -- for the woman saying that the child who fetches her shoes when told she's going for a walk doesn't need ECI? Not so much. My daughter ALWAYS responded to requests. She's autistic. We thought that meant she was ok, too. Your experience is not global.
A., all I can do is tell you what I would do -- I would get the eval asap, just because of my past experiences. Everybody told us that our oldest was fine, because slow-to-talk ran in both our families, etc, but she ended up being autistic -- Early Intervention would have helped her tremendously if we'd known. My next one was so different from her sister: she seemed a little behind others her age, but nothing that required services (so we thought, since we'd had so much experience with them by then). But when she started school, it became clear that she was enough behind to require services after all. She had some trouble with the first couple of years of school because of this. Our new little one, now 14 mos, we are going to rush to EI at the first hint of delay -- we've learned our lesson!
I was a bit uncomfortable with anyone coming to my house as well. Most don't judge, but we did have one come to our house once to do paperwork (right after we had moved and the place was a disaster -- at least we had an excuse then!) and she most DEFINITELY judged. But she was nasty in general, and most definitely NOT the norm -- she was the only person we've ever had difficulty with throughout the many years with both kids in two different school districts. She was gone by the next year from the program and I'd found out later there had been many complaints about her. She was an aberration.
As for the people coming to do the eval, they are the least likely to judge, or even care, about your home or parenting style, imo. They get the best results if your child is in a comfortable setting. They are there for your child only, to see what she can say or do, and in my experience, they are the nicest bunch. (Maybe the nicest bunch of people you'll ever meet, anywhere.)
If you can't get an eval somewhere else, then maybe just bite the bullet and let them come...it could be in your child's best interests. But I understand your trepidations! Still, it's worth it to rule it out. Just because some kids do okay without EI doesn't mean all kids do, and it's better to have it than to not have it if you need it. You won't know without an eval. Hope this helps!
(Though honestly, I've never understood why they need to do paperwork at your house -- I can't help but wonder if this is their way of spying on you to see if your parenting skills are the reason your child is behind. At least it felt that way with that one woman!!)