The Levites have a special "cohinem" gene on the Y Chromosome. It's real easy to find them. There are, in fact, more than enough!
So, does God look down on their sacrifices and accept them?
That's not correct. Among the tribe of Levi, only the Kohanim were allowed to touch the temple furnitures. They were the son of Kohath, and God chose them out of the tribe of Judah to be responsible for the Tabernacle furnitures. So the modern day "Cohen" have a identifying Chromosome that identifies their clan. Thus, when temple worship is re-established in the next re-built temple, the Cohen will be the priests in charge of the Temple articles: The Candle Stick, table for shewbread, the trumpets, the priestly robes, the altars of sacrifice and incense, the lavers, the anointing oil, the incense, and the wash basin.