I highly doubt that. If we're talking about scientific racism, Maghrebi people were always considered a branch of the white race (albeit with varying levels of black African ancestry otherwise found only in Southern Italians and some Iberians). Between their facial features and skin color (not the same as any European groups to my knowledge), Neanderthals would be correctly identified as incredibly "primitive" and probably labeled as some failed offshoot of the ancestors of humans. This is the same era that brought us this cartoon that portrayed the Irish as closer to Africans than good Englishmen and Germans on the basis of skull shape:it would be interesting I think.
Neanderthals are white tough, so to europeans they could be considered less foreign then magreb or african decended people.
The biggest give away could have been the voice but who knows if todays representation is correct, funny thing that from all the jobs neanderthals could do producing a decend falsetto is one of them
Other Europeans with "Asiatic" traits like Finns, Hungarians, and Slavs faced similar discrimination at times. There's absolutely no way a living Neanderthal wouldn't be portrayed as non-white in scientific racism, and probably on the same level as Africans or Australian Aboriginals were as closer to monkeys than white people. Undoubtedly there would've been a LONG history of discrimination against them since no matter which way you put it, there's something very "off" about that face, and that's the browline, cheekbones, and ears. The difficulties of hybridising with H. s. sapiens would also be known. IMO they'd probably have been a slave/servant race most of history given their muscles.
One slight note, that's the maximum number, in practice almost everyone has far less because a limited number of marriage partners and practical concerns like inheritance made marriages between cousins relatively common.One has 1024 (Great)8 Grand-parents and 1,048,576 (Great)18 Grand-parents, the latter being only 560 years or the time of the (so-called) Wars of the Roses (watch Mary Worsley's show on said war), so statistically it's almost certain that I have Baltic Prussian ancestors.