SAN FRANCISCO — As a Mexican-American woman who started her own consulting firm in Los Angeles, accountant Sonia Luna has taken advantage of programs aimed at helping minority- and female-owned businesses compete for government and corporate contracts. But increasingly, the fact that Luna is a lesbian entrepreneur hasn't hurt, either. Federal agencies, organizations such as the National Football League and more than one-third of Fortune 500 companies are trying to expand their vendor pools by explicitly encouraging bids from gay, lesbian and transgender contractors. The little-known outreach efforts mirror longstanding “supplier diversity” initiatives aimed at developing economic opportunities for businesses...