After being refused the knowledge of Brahmastra from his guru Drona, Karna went to Mahendragiri and approached Bhagwaan Parshuram. Karna told Bhagwaan Parshuram that he is a Brahmin of Bhrigu’s lineage. 

There was no reason for Karna to lie to Bhagwaan Parshuram here. Many people claim that Karna had to lie to Bhagwaan Parshuram, because he taught only Brahmins and would have refused to accept Karna as his student had he approached him with his true identity. 

First of all, this claim itself is inaccurate because one of the most famous disciples of Bhagwaan Parshuram during Mahabharata era was Bhishma, who was a Kshatriya and not a Brahmin. 

When Karna’s true identity was revealed to Bhagwaan Parshuram, he essentially told him that, “the knowledge that you have acquired through your lies will be forgotten to you when you face your nemesis.” 

There is no mention of Karna being cursed because of his caste, he was cursed because he lied to his guru and the curse was in accordance with the crime.

You can watch this in video format as well - https://youtu.be/fZ1eHxo6HXs