Compelling state interest only applies to laws that restrict a constitutional right. It can be argued that there are competing constitutional rights here; therefore no "compelling state interest" test. I would argue that if the business has competitors that will provide substitute services, no rights have been infringed on LGBT's. However, it's certainly murky enough so a judge can rule any damn way they want.
In your second example, unless you have a written contract you are an "at will" employee, subject to the will of your employer, unless you are a protected class, (race, Viet Nam Vet, etc.). But don't trust me, Honda says I never went to Law School.
BTW, I am unaware of any employment case where a court protected the employment rights of a Viet Nam Vet. So much for "caring" about Vets. Just another law to get us to vote for Patty "If I Only Had a Brain" Murray, even though she votes against every piece of meaningful Veteran legislation.
