Several rabbis have told me that it is prohibited to give terumah to a cohen nowadays since we are all tamei meit. Isn’t there a fundamental difference between when that law was written and nowadays? Back then there was a beit ha-mikdash, but nowadays there isn’t, so there is no nafka meena whether we are tamei or not?
Although the Mikdash does not stand — may it speedily be rebuilt — terumah, even nowadays, has the status of kodashim. It is considered “holy,” and therefore must be eaten in ritual purity. Because today’s cohanim are assumed to be ritually impure, it follows that they may not consume terumah, even today.
Another reason for which terumah is not allocated to cohanim is on account of possible doubts over lineage.