The Supreme Court’ s conservative majority seemed to be searching Monday for a way to allow religious business owners to opt out of providing certain kinds of services to same-sex couples, while avoiding overturning decades of precedents that prohibit discrimination among customers based on factors like race or gender. By the end of nearly two-and-a-half hours of arguments over a case involving a Colorado web designer who opposes same-sex marriage on religious grounds, the justices seemed likely to back the designer, but precisely how the court will constrain its ruling to avoid broader effects remained unclear. Much of the high court hearing focused on what constitutes speech and who is doing the speaking, specifically whether designer Lorie Smith’s plan for websites that announce weddings for her clients and display their individual stories represent her own speech as the creator.