What does “#Race together” mean? Is this a perfect English sentence?

Solution 1:

#RaceTogether was proposed by the CEO of Starbucks. He said that, in light of the racial issues affecting the United States, Starbucks baristas who normally write customers' names on cups could instead use the hashtag to make for healthy, thought-provoking dialogue on racism.

In terms of the phrasing of "Race Together", it appears that this is a thought to challenge the trends of #blacklivesmatter, #muslimlivesmatter, etc. Rather than address race bit-by-bit, it appears that this would make it an "everyone issue." Instead of race being a minority topic, it's an all-people topic. It also sort of plays on the idea of one race: the human race.

For the specific phrasing, it appears to be one coined by Starbucks Marketing/Communications teams to have a branded voice in these trending topics.

Here is a recent article on the topic.

Here is the original video.