Service can be refused when there is an alternative
If an individual feels they cannot render a service, there must be an alternative
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If we want to find a compromise that helps preserve religious freedom but also allows same-sex couples to have full access to the institution of marriage and all that it entails, this might be the most equitable way of resolving the dispute.
This question balances two opposing rights - the baker's right to religious freedom and the couple's right to a service. Religious freedom is something we hold dear - we even allow people to risk their lives by refusing blood transfusions or helmets. So this is an important right that we want to preserve. On the other hand, the right to not be discriminated against and to marry is also important - it may not seem significant to be unable to get floral arrangements for your wedding but for many people, it isn't really a wedding without a cake or flowers. There is also the matter of the enormous emotional strain of feeling like a second class citizen every time you are refused service. It seems like an obvious compromise therefore to allow bakers to refuse a same-sex couple service if they can access that service in another place. It allows for both rights to be preserved even if it does allow for some discrimination. The real-life implications of this is that most service-providers will be able to refuse service because there is a significant wealth of other providers. In small communities however, where there is one cake-shop or one florist, that baker/florist will have to provide that service. In that case, we deem the principle of non-discrimination more important than preserving religious freedom to opt out. This may not be that important in the case of florists or bakers (although I have explained why it might also be quite crucial) but the case of clerks and attorney who provide marriage licenses is quite different, and shows why this is an important compromise. If the only marriage office in the city refuses to issue you a marriage license, you are effectively prohibited from marriage even if it is legal in your state, particularly for lower income individuals who may not be able to travel into a different jurisdiction.
What this argument assumes is that there will always be a way for couples to access the services that one service-provider denies them. This may not be true. One problem is that it is difficult to define at what point the couple would be denied of the service. How do we tell what a reasonable alternative is - is 50km further okay? What about 100km? If everybody in your town refuses to serve you, how far out would it be considered an acceptable distance for you to go?
P1. Whenever possible, we should aim to preserve religious freedom P2. Religious freedom is not as important as freedom from discrimination in accessing services P3. It is possible to access services in ways that don't impinge on religious freedom C1. Whenever possible, we should access those alternative services C2. If that is impossible, religious freedom is less important than freedom from discrimination
Rejecting the premises
P3. It is possible to access services in ways that don't impinge on religious freedom To what extent this is true is contestable.