When rights are in competition (in this case, the rights "religious believers" vs. the rights of members of the LGBT community), an old axiom is helpful (perhaps not decisive in every case, but helpful): My right to swing my fist ends where your nose begins.  In the exercise of my rights, I may not harm you or deprive you of yours.  
As a matter of law, members of the LBGTQ communities cannot be disadvantaged in the public square -- in government, business or commerce.  A member of a minority community ought not have to wait even five more minutes than anyone else to obtain a marriage licence; or go to the next block or the next neighborhood or the next town to purchase goods or services that are available to everyone else -- though obviously they may choose to do so.