MLK was hated by many at the time. To see why, just look at the comments opposing BLM today. They are conspicuously similar in tone and content.
Many of the attacks are the same, but today there's an odd rhetoric that attacks what BLM does with an imaginary myth that protests during MLK's time were wholly peaceful (they weren't, and were also derided due to violence at the time).
You present a good argument, but it falls flat before simple facts. MLK left images of crossing the bridge dressed as an accountant. BLM left images of a riot.
Anti-BLM propaganda does not even have to work hard. All it needs is amplification.
The question of violence is how often it occurs on a broader scale. I live where there were many, many protests and little violence (and often the violent ones were outsider instigators and criminals looking to create it, not civil rights protesters).
https://www.smithsonianmag.com/history/black-protestors-have...
If you want to continue trashing BLM, maybe look into how MLK was received in the 60s. There are a lot of people trying to amp up myths to intentionally use MLK to disparage BLM. Make sure you're not unintentionally getting caught up in that.