Is mistaken identity a hate crime?

The man shot in Washington state last Friday by an assailant who reportedly told him to "get out of the country" was almost certainly mistaken for a Muslim because, as a Sikh, he wore a turban and a beard. Muslims are identified with turbans (hence the "towelhead" slur) but to my knowledge none of Islam's silly dress codes require men to wear them. Sikhs, however, are expected to wear them, which puts them in danger from ignorant people in this country. The victim will survive, fortunately, and meanwhile his family reportedly wants the case prosecuted as a hate crime. A case like this would really clarify the status of hate crime as thoughtcrime, even though the shooter (who remains at large) may not even have an opinion of Sikhs, unless he's an indiscriminate xenophobe. The idea that he hated somebody apparently would be enough to make his crime more deplorable than it already is. In the unlikely event that he did act out of specific hostility to Sikhs, he'd be out of step with President Trump, who has done some outreach to India and Americans of Indian descent, probably recognizing that Hindus, at least, are as certain allies in a war on Islamic terrorism as anyone you'll find on Earth. Over the weekend the President condemned the recent killing of another Indian man who somehow was mistaken for an Iranian by his assailant. It's in his interest to highlight non-white victims of radical Islam around the world as the best way to show that whatever measures he intends to take are not motivated by "racism" or raw nativist xenophobia, while idiotic acts like last Friday's shooting only confirm many people's suspicion that too many Americans hate any form of otherness, regardless of what those others think or believe. With luck, this can become an educational moment on all sides, but that might be wishful thinking by now.