Are we morally obliged to boycott businesses that support abortion or that grant same-sex benefits to employees?

You are under no moral obligation to boycott a business that offers morally good or morally neutral products and then spends its proceeds in a morally objectionable manner.

What can be done, and what many pro-life people choose to do (they are not morally obliged to do so), is to band together with other like-minded consumers and refuse to buy from one particular business to encourage that business to stop supporting a morally objectionable practice. Boycotts, when done in a responsible manner by concerned consumers seeking social justice, can be meritorious actions. But people are not morally obligated to join them.