While the Black Lives Matter movement has seen an uptick in support from people of all races and backgrounds, the movement is still a predominantly Black movement.
The movement has received unprecedented support from companies, politicians, and everyday Americans. But those who join and support the movement at one point often choose to distance themselves from it or stop speaking up at another point. There are many who hail a social justice movement until it "goes too far" or starts making "unreasonable demands". 
Many who don't agree with violence and rioting see that some protesters are engaging in that behavior and choose to withdraw their support.
Black Lives Matter is a predominantly Black movement because it has the unwavering support of the majority of the Black community, even in times of trial and tribulation. Black lives will always matter to Black people - not just sometimes, or once in a while, but all of the time.