BLM protests Buttigieg because when he was mayor, black officers fled his police department because of racism within the department. The perception is that.Buttigieg did little to prevent the exodus.

In January 2012, Pete Buttigieg stepped into the South Bend, Ind., mayor’s office after winning the city’s first open mayoral election in 24 years. South Bend had three African Americans in visible high level and public leadership positions: Mayor’s Assistant Lynn Coleman; Fire Chief Howard Buchanon and Police Chief Darryl Boykins. 

Within three months, all three would be gone.

https://www.theroot.com/mayor-pete-s-invisible-black-police-1840727624

Buttigieg is viewed as having conducted a war against the homeless.

With 14 percent of the city’s housing vacated or abandoned, Buttigieg had a task force identify every relevant property and recommend an overall course of action. Its conclusion? That the city should slap fines on homeowners to incentivize repairs and empower officials to demolish derelict properties at the owner’s expense. But it just so happened that most of the vacant homes were in low-income black and Latino neighborhoods, where some city residents had housing from deceased relatives or were still listed as owners despite having been forced out by pricey mortgages.

According to South Bend’s own records, in fact, both the fines and demolitions meted out thanks to the mayor’s policies tended to be heavily concentrated in these neighborhoods (one resident, for example, reported being fined thousands of dollars between 2012 and 2014 for infractions such failing to mow the grass).

South Bend’s eviction rate, meanwhile, doubled between 2012 (when Buttigieg was first elected) and 2016, now sitting at three times the national average. 

https://jacobinmag.com/2019/06/mayor-petes-war-on-the-homeless

Edit to add:

Former vice president Joe Biden is far and away the favored candidate for the Democratic presidential nomination among black Americans, boosted by his personal popularity, his service in the Obama administration and perceptions that he is best equipped to defeat President Trump, according to a national Washington Post-Ipsos poll.

Sen. Bernie Sanders (I-Vt.) occupies second place in the Democratic field among African American voters, easily outdistancing the remaining candidates in the race. Sanders is leading among black voters under age 35, replicating his success with younger white voters in other national polls. Sen. Elizabeth Warren (D-Mass.) runs third.

The survey finds meager support for former South Bend, Ind., mayor Pete Buttigieg, who is among the leaders in polls in the predominantly white states of Iowa and New Hampshire but stands at 2 percent among Democratic black voters nationally. A lack of familiarity with him and concerns about his experience and sexual orientation appear to be contributing to his current standing. Buttigieg has said that as African Americans get to know him, he will gain more support, but the poll undercuts that assertion. He receives only 3 percent support among black voters who are familiar with him.

https://www.washingtonpost.com/politics/biden-holds-wide-lead-among-black-voters-in-democratic-presidential-race-post-ipsos-poll-finds/2020/01/11/76ecff08-3325-11ea-a053-dc6d944ba776_story.html