It's private property. If that manager is running that shop, he/she can ask anyone to leave for any reason. The police asked the men to leave Starbucks at the request of their manager and the men refused. From a legal standpoint, they were trespassing for remaining in Starbucks after being asked to leave.

Like someone said in this post, it's the optics that are gonna kill Starbucks. I don't drink coffee so I've only ever been in a Starbucks a couple times with the lady. But don't they tend to have people camped out for hours, using the wi-fi and nursing a single cup of coffee?

The story is that these men weren't doing anything offensive or disturbing. Its apparent that he/he picked them because they were big, scary black men and that's why she asked them to leave. If this is how Starbucks treats people (which they are legally allowed to do), they're gonna get slaughtered in the court of public opinion.