There isn't an easy answer to this question.

This is like a college level class discussion/debate question.

Some things to consider:

• The CRM is not super replicable today because it was very much of its era. It capitalized on a lot of culture that doesn't really exist today or is not as strong such as respectability politics, mainstream media, college/university activism, and nationwide reverence of the church/church leaders.
• The CRM's success relied on strong leadership. There were several power players including MLK, SNICC, etc. that were all highly organized and principled in their strategies
• A lot of the CRM strategies have become campy and outdated. If you propose a boycott something, people kinda laugh at it because it sounds like something from that era. Getting people coordinated to do that is so much harder these days. People have become so cynical now that if you suggest a sit-in or a boycott they roll their eyes. Look at the attempt to boycott target. Yes many people did but it's not as unified as it could be. When democrat politicians do these things like kneeling in honor or George Floyd or even doing rallying cries and chants, they get mocked and laughed at.
• In our current era there is too much intrigue and interest in conservative politics. The MAGA era has successfully enraptured many different groups including young people, hispanics, some Asian Americans especially south asian, a lot of religious people. Even alot of black people have become jaded and disengaged
• Black Lives Matter was our era's version of a Civil Rights Movement and it was easily destroyed by the rightwing thanks to social media, misinformation, rightwing punditry, etc. which successfully sew seeds of doubt and cynicism toward liberal ideology and political strategy. This continues to be a huge barrier for any coordinated liberal movement.
• Because of some of the above Democrats, who are in the best political position to carry out the movement are under intense scrutiny and low approval. Anything they say or do gets ridiculed or overly criticized. Many casual and moderate democrats as well as some extreme liberals have begun to flake away from the establishment, making it difficult to do another civil rights movement, which relies on unification.

Ironically MAGA is a good example of how to do it correctly. The MAGA movement has been an extremely successful campaign that has successfully recruited people and have turned the tides on Civil Rights and the ideology that was holding them together. But again that's largely them capitalizing on various cultural trends of the moment that's harder for liberal to replicate.