http://www.npr.org/2017/02/28/517092031/in-religious-freedom-debate-2-american-values-clash

There is both audio and text at the above link. From the text:

"The debate's heart: What "exercising" one's religion means

Under the First Amendment to the U.S. Constitution, Congress is barred from enacting "an establishment of religion," but neither can it prohibit "the free exercise thereof." The question under current debate is what it means to "exercise" one's religion.

If a football coach is not allowed to lead his team in a public prayer, or a high school valedictorian is not given permission to read a Bible passage for her graduation speech, or the owner of a private chapel is told he cannot refuse to accommodate a same-sex wedding, they might claim their religious freedom has been infringed. Others might argue that such claims go against the principle of church-state separation, or that they undermine the rights of LGBT people to be free from discrimination.

Legislation either to uphold LGBT rights or to limit them in the name of protecting religious freedom has advanced in several states, and further court battles are likely."

Though the story doesn't fully state it, the conflict is between the U.S. Declaration of Independence's first line ("All men are created equal") and the U.S. Constitution's Fourteenth Amendment's due process clause versus the U.S. Constitution's First Amendment which, while telling government not to support a specific religion, allows all men (persons) to believe and worship as they please.

This conflict has been going on for a long time. For example, the law enacted that ultimately forced the Church of Jesus Christ of Latter Day Saints to stop polygamy could be read as a direct challenge to the First Amendment's ban on government's not endorsing a specific religion as well as an attack on allowing people to believe and worship as they pleased, no matter how bad polygamy was (and it was/is really bad, especially for the women and children involved).

but how can I be offended by their existence?

If a Muslim walks into a Hindu owned building would it (technically) defiled? Can evangelicals deny employment to atheists or Wiccans? Just because you trade with sexual minorities will you be cursed and go to Hell? Where does this end? I don't know but you have to fair open commerce for all or everything would just stop.