Here I will post papers showing that the canonical example of Hungarians where linguistic shift supposedly occurs by small elite (mostly males) imposing a new language is a myth.
The ancient mtdna of early Hungarians had much more Eastern mtdna than modern ones.
102 ancient mtdna were tested and here is the result. Notice women theoritcally should not be part of warrior horde. Yet they were present there.
And here the y dna results for the same ancient Hungarian Conquerors
Notice that N which is rare in modern Hungarians was the most frequent one among the early Conquerors. You can add also R1a Z93 and C2 as other possible markers of eastern impact.
As one can easily note that Slavic people didn't shifted to Hungarian language just because it was just a new cool language.
There was a serious genetic impact, which was washed away later for socio-political reasons.