"Only white people" is what I'm going off of. That would mean no Asians, no natives, no middle eastern people. Just whites.

The whites would survive, but the world would be a different place and a lot of them would die from starvation and/or some inability to adapt to the world suddenly without people of color.

That would be true even if the 6.5 billion or so people that evaporated from the planet were chosen indiscriminately of race though, but given the vocational specialization of white vs nonwhite people then it would be worse for the survivors right at the beginning in the whites only scenario.