When the Black Lives Matter movement started, they didn't have the support of a majority of the population. That has changed. Now both of these polls show that a majority of Americans now support the movement.
The top chart reflects the results of the Civiqs Poll. They have questioned 106,452 registered voters on this issue since April of 2017. The latest survey, done on June 10th of 2020, shows that 53% of registered voters support the movement, while only 26% oppose it. And every demographic group has more supporting than opposing -- every group but one (Republicans).
The second chart is from the Pew Research Center. They question 9,654 adults nationwide between June 4th and 10th, and their survey had a margin of error of only 1.6 points. It also shows every group with majority support -- except Republicans.