For example, if pressed, about as much as you could get from an evo biologist is that what distinguishes difference between species is their inability to interbreed.
Humans probably could tell neanderthal were "different" but not in a way where they thought they were truly "other".
If anything, humans tend to be more prone to look for differences than assume equality.
Note the humans and chimpanzees diverged like 5 million years ago. Neanderthal is very close to us and it's reclassified as it's own specie or as the same specie from time to time.
There is a nice graphic in https://en.wikipedia.org/wiki/Chimpanzee%E2%80%93human_last_... Neanderthal is not in the graphic, but if you want to add it, you should put in near the top left, between us and H. Erectus, probably closer to us.
I always recommend one of my favorite essays for this topic: “The categories were made for man, not man for the categories”
https://slatestarcodex.com/2014/11/21/the-categories-were-ma...