The Washington Post explains:
The case can seem deceptively simple: Since patrons of tanning salons are almost exclusively white, the tax will be almost entirely paid by white people and, therefore, violates their constitutional right to equal protection under the law.
But it's not, according to the Post. Since there was no intention of discriminating by the government, charges of discrimination can't be filed.
If only lack of intention excused so many other sorts of behaviors...