where is the balance between religious freedom and the rights to service?

I have a strong desire to preserve both but they seem to tugging against each other in this case.

I started by looking up the sign I have seen in most every service related industry since I was born:

"We reserve the right to refuse service".

I wondered if this is true, or just a sign...

http://www.legalmatch.com/law-library/article/restaurants-right-to-refuse-service.html

So Are "We Reserve the Right to Refuse Service to Anyone" Signs in Restaurants Legal?

Yes, however they still do not give a restaurant the power to refuse service on the basis of race, color, religion, or natural origin. These signs also do not preclude a court from finding other arbitrary refusals of service to be discriminatory. Simply put, restaurants that carry a "Right to Refuse Service" sign are subject to the same laws as restaurants without one.

What Conditions Allow a Restaurant to Refuse Service?

There a number of legitimate reasons for a restaurant to refuse service, some of which include: *Patrons who are unreasonably rowdy or causing trouble *Patrons that may overfill capacity if let in *Patrons who come in just before closing time or when the kitchen is closed *Patrons accompanied by large groups of non-customers looking to sit in *Patrons lacking adequate hygiene (e.g. excess dirt, extreme body odor, etc.)

In most cases, refusal of service is warranted where a customer’s presence in the restaurant detracts from the safety, welfare, and well-being of other patrons and the restaurant itself.

But this doesn't cover religion at all! Is there any precedent for refusing service on religious grounds anywhere?

http://www.guttmacher.org/statecenter/spibs/spib_RPHS.pdf

Sparked by the U.S. Supreme Court’s 1973 decisions in Roe v. Wade and Doe v. Bolton that legalized abortion nationwide, federal and state governments have enacted laws that allow health care professionals and institutions to refuse to provide services related to reproductive health without facing legal, financial or professional consequences.

A patchwork of federal laws explicitly allows many health care professionals and institutions to refuse to provide care related to abortion and sterilization services. Collectively, these laws prevent government agencies from forcing the provision of services or “discriminating” against individuals and institutions that refuse to provide them; they also prevent institutions receiving certain federal funds from taking action against health care personnel because of their participation or nonparticipation in beliefs about abortion or sterilization. Separate federal laws and regulations, notably Title VII of the Civil Rights Act, prohibit employers from discriminating against personnel based on religion, including religiously based objections to performing specific job functions; an employer must reasonably accommodate an employee’s religious practices unless doing so would impose an undue hardship on the employer.

....

In large part because of the introduction in the United States of emergency contraception in the late 1990s, the issue of religious and moral objections to providing care has expanded beyond doctors, nurses and hospitals to include pharmacists and pharmacies. Since that time, a few states have enacted laws that specifically allow pharmacists or pharmacies to refuse to provide health care because of religious or moral objections.

http://en.wikipedia.org/wiki/Conscience_clause_%28medical%29

Conscience clauses are legal clauses attached to laws in some parts of the United States which permit pharmacists, physicians, and other providers of health care not to provide certain medical services for reasons of religion or conscience. In many cases, the clauses also permit health care providers to refuse to refer patients to unopposed providers. Those who choose not to refer or provide services may not be disciplined or discriminated against. The provision is most frequently enacted in connection with issues relating to reproduction, such as abortion, sterilization, contraception, and stem cell based treatments, but may include any phase of patient care.[1]

So this is where it seems to me there is actual legal precedence to claim that your religious freedom can be cited as a reason to refuse services.

http://www.huffingtonpost.com/2014/04/07/supreme-court-gay-wedding-photography_n_5104699.html

ALBUQUERQUE, N.M. (AP) — The U.S. Supreme Court rejected an appeal Monday from a studio that refused to photograph a lesbian couple's commitment ceremony, letting stand a New Mexico high court ruling that helped spur a national debate over gay rights and religious freedom.

The justices left in place a unanimous state Supreme Court ruling last year that said Elane Photography violated New Mexico's Human Rights Act by refusing to photograph the same-sex ceremony "in the same way as if it had refused to photograph a wedding between people of different races."

Well, that certainly makes perfect sense to me! People used to claim bi-racial marriage was against their religion too!

I think to research this aspect more, you would need to determine if those same doctors that can refuse to hand out the morning after pill or perform an at-will abortion will also perform an abortion if they feel the mother's life is in danger and the child won't survive, and the mother will not survive without an abortion. It would then illustrate that a doctor who can provide that service for one reason can also deny it for another reason.

Now if a doctor is allowed this right by law - why is a baker not allowed the same right to refuse supporting what they feel is sinful and object to on religious grounds? Does this go beyond the baker (as in the link above) and go to the nanny or the day care center or the private school?

If a person walked into a bakery and ordered nazi cupcakes with swastickas and a giant printed cake of hitler... and that person is refused - is that legal? Do Florists have to provide their services to the Illinois Nazi's wedding? I can't even see these as objections on religious grounds - they would be straight up moral objections! But I can't see anyone in the world saying "Oh no, we need the SCOTUS to force that baker and florist to provide for the Illinois Nazi party!"

I think in the end the judgement comes down that discrimination on sexual preference is against the law, religious belief or no. But your idea that it is hard to see clearly the reasons why is solid. It is hard to see why. These rights do tug at each other. As long as we have a society that regulates opinion - they will tug at each other.