Every few months, social media lights up with a story or viral video about discrimination in home-sharing: A host kicks out a black guest or cancels a gay couple's booking or doesn't respond to a Muslim woman's inquiry. The dominant brands — Airbnb, Booking.com and VRBO — work quickly to contain the damage. They may ban the host, find new housing for the guests and remind followers of their anti-bias policies. But a handful of smaller competitors are trying to ease fears of discrimination by catering to specific minority groups, and this alternate approach has carved out a small but thriving piece of the home-sharing market.