No matter what the scientists say, if Homo Sapiens and Neanderthal could inbreed and produce offspring that could reproduce them selves then they are actually the same species.
If they were different species and inbreed then the offspring would be sterile.
Much like the mule, the offspring of a donkey and a mare is sterile.
/bingo
You may be confusing species with genus. The different Caninae and Felinae species are able to cross-breed. But it’s not always pretty.