The Hungarians in Ukraine (about 200 thousands) live mostly in Transcarpatia, just along Hungarian border. Many have Hungarian passports.Their main town is Beregovo (I visited it, though long ago). As a rule local Hungarians speak Russian but Ukrainian language is in fact useless. Local Ukrainians use their dialect (or Rusin language) that is too distant from standard Ukrainian. Transcarpatian Hungarians will not be assimilated anytime soon. They will use Hungarian language at home and inside their communities. They feel and will feel themsleves as a part of Hungarian cultural space. For them Hungarian schools are something essential and Hungarian government will fircely defend their right for Hungarian schools. It is not a big problem for Kiev authorities. They would allow Hungarian (and also Polish, Romanian) schools easily but ... as a result they would have to allow Russian schools. Abolition of education in Russian is the main objective of Ukrainian ruling circles.
The region was tacked onto Ukraine after WWII, having previously been part of Czechoslovakia. Supposedly Moscow wanted the area to be part of the Soviet Union as the addition of that gave them a direct land border with Hungary, should they need to send troops there. However, the region had no historical or cultural connection with Ukraine. It was another example of the communist heirarchy's arbitrary redrawing of borders without regard to the people living there.
This tends to make the authorities in Kiev very nervous about the people who live there. The recent changes in the language laws may act to alienate the people there, who tend to have more connection with Hungary (via the dual passports which you mention - which are illegal for Ukrainian citizens to have by the way) than with Ukraine.
This could all result in Kiev creating a problem in the west of the country which didn't previously exist.