The consumer funds the artists' actions
When a consumer makes a purchase, they are making an active decision to support a person. The money with which they purchase an album, the statistics that their streams add influence to, all of these things ultimately go to help the artist who committed atrocious actions.
< (1 of 2) Next argument >
When a consumer purchases a product, the monetary value of that product goes to fund the artist. Woody Allen is the one who earns money off of his movies, Kevin Spacey gets paid for the movies that he acts in, and Sherman Alexie is the one earning the money whenever someone purchases a copy of “The Absolutely True Diary of a Part-Time Indian”. What all of this ultimately means is that, even if the consumer might not morally agree with actions like sexual assault, their actions of buying the book speak much louder than their words. Without a doubt, sexual abuse is scarring, and it can traumatize a person for life. Every consumer should be able to understand and sympathize with the horrors of this. Therefore, it is important for everyone to play a part in making sure that sexual abusers are not able to get away with abusing the people around them. It also sets a precedent for future sexual assaulters, showing them the grave consequences of sexually abusing another person and the fact that the market cares and the market will do something about them. When a public figure is boycotted, even if they are still wealthy and powerful, they lose a lot of things like advertising deals and company contracts that feed their power. 
If the artist were truly guilty, they would go through the legal process and be prosecuted anyways, just like Harvey Weinstein was. At that point, the majority of their sales wouldn’t go to them anyways since they would still lose their brand contracts on top of the fact that they would be sitting in federal prison. Additionally, given the fact that many of them, like Michael Jackson, have already passed away, boycotting the art does absolutely nothing to change the outcome of a past event. In terms of the few who are still alive yet have not been prosecuted, given that the sexual abusers that are being exposed in the #MeToo movement are predominantly people who are already in positions of power, a temporary scandal is unlikely to make too much of a dent in their careers anyways. The only way in which boycotting would make a difference would be if they were already facing a losing legal battle, at which point a boycott would delegitimize their image even more. But at that point, they would likely lose in court anyways.
[P1] To purchase an artist's art is to fund their lifestyle [P2] Boycotts are effective
Rejecting the premises
[Rejecting P1] The court system can deal with the artists themselves [Rejecting P2] Boycotts are unnecessary