First, let me congratulate you on asking a very pertinent contemporary question, in a very articulate manner.

Second, may I suggest that some way to "periodize" the question and its answers may help... for example (1) Early Years (2) Late Obama Years (3) Trump Era.

Finally, I ran a "Google Scholar Search" with some keywords and phrases, taken from your question and from what I considered as relevant phrases...

Of course, the results exceed 1800, but if you go through perhaps the first 5 to 10 pages of these results (see Link), you may find a lot of useful sources and materials.

https://goo.gl/Vb53MN

In order for a black life to matter,I must make my own way and life matter. I must vote,continue to get my education most all.I must stay close to God and Jesus for guidelines.

Jael Dolly

If you are seeking an approach the research from an 'applied' cultural anthropological perspective there are vast considerations.

First, there are prerequisites that must be satisfied, the most immediate being, understanding individual and group motivations of the BLM movement, social interactions between members, economics, and most importantly, their worldview as indicated on the "superstructure of cultural systems connected with the infrastructure and social structure guided by the 'barrel model'" (Haviland 297). After all, there are combinations of religious/ spiritual, economic, and cultural reasons people do the things they do. It is advantageous to look at a wide scope of these motivations.

Then there is the even wider scope of law enforcement, the hegemony being of Europid descent sets the tone of social norms in America, indeed, the world. The current formula or policy is the "Broken windows" theory of community policing, an agenda set far apart from goals of the BLM movement. 'Zero tolerance' for social deviance is bound to impact protests, peaceful or not (Alpert, et al., 2016). As such, the butting of heads between BLM and police is inevitable. However, priorities established by local and Federal legislators does little to distinguish or address policies that conflict with critical social movements and policy directives.

From those understanding qualitative data research and analysis should challenge your resolve to be sociologically mindful of culture-bound fallacies.

ALPERT, G. P., DUNHAM, R. G., ALPERT, G. P. AND DUNHAM, R. G.

Critical issues in policing: Contemporary readings Seventh Edition

Haviland, William A. Cultural Anthropology: The Human Challenge, 14th Edition.

To best study this research question, I suggest that you interview or survey police officers in the areas that are most affected by this movement, such as Ferguson and Baltimore. 

Considering the question involving BLM's impact on law enforcement, a worldview is necessary.  From 2017 and before, political events are playing out with increasing uncertainty.  An uncomfortable number of African American and Latino citizens support the current administration for various reasons.  That so many minorities think conservative views are possible without condemnation of White supremacy is normal is baffling.

In spite of the Black Lives Matter movement, Federal and State legislators stay complacent and disdain citizen complaints.  Now dismantled, the earlier justice department implemented measures which could help offer solutions to social problems affecting minorities.  Embolden racists supported by the Republican party to collude with safety officers to exact ethnocentric principles to suppress liberals.  

The Police have geared up to engage movements that challenge them while enjoying the full support of their superiors.  Caucasian hate groups are aggressive and seek a race war under the gist of supporting against disorderly minorities while law enforcement applauds them.  The human problem is revealing itself with every murder of a minority, and with every retaliation brings with it desperate social change.

Black Lives Matter affected the choice which law enforcement must make, an impact on loyalties and commitment to help or destroy conditions that preserve life, liberty, and equality.