The news of late, including commentary about the dissension between Liz Cheney and other House Republicans, is that the holdup on getting a commission to look into the Jan 6 insurrection is that the Republicans are insisting that such a study include looking into BLM riots. Democrats (and Liz) rightly argue that the Jan 6 event was a one-off, unprecedented in our history, but Republicans are locked into their support of Trump’s big lie and will not agree. My guess is that the Republicans think the BLM portion of the investigation will find things to embarrass the Democrats. It seems to me much more likely the findings would be mixed, with lots of material the Republicans would not like.
It seems to me there is a way out of this cul-de-sac, and that is for the Democrats to accede to the Republican position, but set the BLM commission up as a separate entity. That would cut the legs from under the Republican position, and allow each study to focus on the disparate issues while eliminating the potential for conflation of irrelevant material.