I don't expect any clear evidence. I expect that outdoor gatherings are fairly safe, especially in warm weather.
If there were no arrests, I'd predict no correlation with COVID-19 trends after adjusting for factors such as income and race. Crowded jails likely create some problems, but if jails spread the virus, that doesn't tell us much about health policies.
I think the demographics of protesters does not have as much cross over with those tested for COVID-19. Until testing of asymptomatic is done with good random sampling, I couldn’t really say for sure. However it is possible that the younger protesters may not show symptoms after this, won’t get tested, and won’t influence post protest case rates. On the other hand, protesters are more likely to from the hardest hot populations: black, hispanic, poor, living in a shared living space, lacking health insurance, and the other factors found to be disproportionately effected from this disease (and others, they also have the most comorbidities which contributes to higher death rates). Thus protesters may have higher immunity rates than a randomized sample. Overall I think this underestimates the effect of lifting the lockdown, but is still weak evidence of course.
[Speculating on a hypothetical.]
Looking at some of the images in the news regarding the ongoing protests sparked by the latest death of a black person while in the hands of the police seem to suggest social distancing is not really a primary concern for the protestors or the police.
As we look at the COVID-19 statistics in the next few weeks one might expect to see a second wave originating from that event. If a second wave is not very pronounced or noticeable, what might be the implication for public health policies? A strong update on prior or some other type of response?
Not asking what the response should be but more for predictions about what they will be, given the assumption of any resulting second wave occurrence.