Their joke is that, based on their last name, the person saying no to refugees is an immigrant themselves.
based on her last name, assuming she is of indian descent so presumably he is talking about the irony of a european refugee not being allowed into a britain because of a brown person
This sort of thing isn't all that unique either.
She's a vile politician, thats probably the joke
Because of her ethnicity, she isn't allowed to be really British to racists, and especially not allowed to be a Tory. By masking that racial attack in sarcasm, you can say it without identifying yourself with it.
By definition she's not British, she might be a citizen of the UK but she's not racily part of the ancient people indigenous to the island. Some of the people (including immigrants) are starting to understand the problems this causes.