hungarian and romanian are - on historical scale - both pretty new cultural concepts. you can not debate that these cultures were created by magyars and romanians, and their cultures (and other middle-eastern european cultures) effected/helped eachother's culture more or less in the centuries before. and ofc. you can not debate that people today identify themselves (and their ancestors) with their culture. and - today - you can easily bind a nation with a culture.

and you are absolutely right, when you say, that our present day opinion on these issues were formed by politicans and social scientists, rather than archeologists and cultural scientists. luckily, either our apetite for knowledge grew this out, or the different scientific directions are finally closing to eachother.

what do "scholars" know about more thousand year old nations and cultures?

we know cultures from different eras, and we know nations from different eras. there are cultures we can bind to a nations, and we can say which nation - or nations - was their carrier. and we know about cultures, we can not bind to any nation (yet).

lets skip the apes, and the caveman, and the cultures of the stone age (~35.000 BC). we could have a great discussion about their cultural or national identity, and we both would be right, but not on a scientific scale.

the fertile lands and the presence of water sucked in different nations. farming and animal husbandry was popular. if we can belive archeologists, the first culture that ruled Transylvania (and the Carpathians) and is worth mentioning is from the stone-copper age: the Tiszapolgár Culture (~4.000 BC), that was followed by the Bodrogkersztúr Culture (~3.000 BC).

from this era, its easier (or the only possibility) to identify cultures with time periods, rather than nations.

thanks to a climate change a migration period started, the nations from the copper age moved on, the newly arrived nations took only part of the former culture: animal husbandry became dominant.

bronze age comes with the Beaker culture (~2.000 BC). and if we can belive our eyes: there was an iron age (~1.000 BC) nation in ~Translyvania, that we know by name (only an exonym, the greek called them): the Thrace. We know different celtic and scythian tribes from this era too, by name.

from the 1st c. BC the Roman Empire extended its borders, firstly to Pannonia and then to Dacia. the different tribes (or nations), already living in the Carpathian Basin mixed with the romans, and were culturally latinized (romanized).

after the fall of the Roman Empire, in 4th c. different tribes - chased by the Huns (not hungarians) - seeked and found shelter in the Carpathians, Goth and Gepid tribes settled in Transylvania for a good century, but they were conquered by the newly arriving horse riding, half-nomadic Avars.

the national and cultural consistency of the Avars is still an open question. no one looked in it seriously. there is a proverb about it: Disappeared, like the Avars.

Slavs arrived, in the next wave of migration, and settled in the vast, empty regions, just to be conquered by the Magyars, arriving a century later.

there is no history about another massive migration or a genocide (Avars, Slavs or Hungarians probably assimilated the previous tribes) till the Mongol invasion of Europe, so we can belive, that the same people lived in the Carpathian Basin (and in Transylvania) from the fall of the Roman Empire till the Mongol Invasion of Europe.

and since we were conquered and occupied by the same overlords, we can say, that we are - by blood - all the descendants of the pre-celt/pre-slav/pre-hungarian nations(tribes), but some of us ended up with different culture than the others.

oh, the question: the Avars, Slavs and Magyars arrived to an almost empty Carpathian Basin, the former Roman Cities were ruined, the inhabitants scattered, Transylvania must have been ("culturally") 100% Magyar at the time of the Hungarian Conquest, and the next time the culture could have shifted was at the Mongol Invasion of Europe and the Ottoman Invasion of Europe - because both of them clearedentire regions swallowing wealth and inhabitants aswell.

edit: typo