In response to the three questions:
A business owned by an obervant Jew would not be open on Shabbat. This is a matter of personal faith and not discrimination. Businesses may choose to close on a given day for religious or personal reasons. Few businesses are open Dec. 25, for example. It's only an issue if, say, a business says they will deliver to straights but not gays, or to whites but not blacks, etc. The closed Jewish business is equally closed to all potential customers (as would be a Muslim owned business on Friday or Christian owned business on Sunday) so there is no discrmination.
Would a Muslim cab driver be required to allow a seeing eye dog? Absolutely. By law service dogs must be allowed anyplace their human is allowed, including places like food stores or restaurants where normally dogs are not allowed. These dogs are very well trained and don't relieve themselves in improper places. To refuse to allow a person with a service dog into a taxi or anywhere else absolutely is discriminatory, not against dogs (dogs legally have no civil rights) but against people with disability, a protected class under federal and many state laws.
Could a gay business refuse to print flyers for Westboro Baptist? A bit gray. If the business refused to print flyers for Christians generally or for Baptists specifically that would be considered an act of illegal discrimination. But if a business (gay owned, straight owned, or whatever) declined to print political materials for a political event (like a picket or demonstration) they opposed, it probably would be legal in most states. Some states prohibit employment discrimination based on political affiliation, but I don't know of any (I may be wrong) requiring a business to supply service for politics they disagree with. Public services are different; the Post Office may not refuse to mail the material, for example, and police must provide protection. (Under Arizona's defeated bill, there would be no such requirement for service to gays.) I just reaq about a woman who declined to make a wedding cake with a hunting theme, due to her animal rights beliefs. So far as I know there is no legal issue.
Funny, whenever I conflate "Christian" with "antigay bigot" someone always tells me that not all Christians are antigay bigots, but in this thread we hear gays are trying to shut down "Christian" businesses. The majority of businesses in America are owned or managed by Christians. Gays are not trying to shut them down.
As to it being so evil and unfair to "make" a bakery make a cake - which after all is what they are in business to do - a poster summarized law on who could be admitted to restaurants (or excluded) and this is generally correct for American business. A bakery could also be legally shut down if they refused to provide the cake for an interracial marriage. Or a marriage between senior citizens, or people with disabilities. Because there is NO LEGAL RIGHT TO DISCRMINATE (except against gays, legal in 39 states) based on race, religion, age, disability, sex. You may think the students who sat in on lunch counters were wrong and the restaurants with white only signs were right, but history passed you by half a century ago.
As to why a same sex couple would go to a bakery, florist et al that hated gays, well, in cities there are lots of options, but in small communities there may be only one bakery in town that does wedding cakes. I doubt, frankly, that these couples went out of their way to seek businesses that would insult them while they planned their special day.
As to Jason Collins - I'm so glad he's not a Laker!
P.S. A sportswriter in today's SF Chronicle pointed out that if Michael Sam was drafted, and his team played in the upcoming Phoenix Super Bowl, the law that was recently vetoed would have permitted the hotel owner to refuse to rent a room to him. Like Black players in earlier years. I doubt that would happen, it would be phenominally stupid for the business, but legally, yes, it could have happened. And as to the legislators who said they did not know what the bill really said, it was not some 2000 page tome, it was a short bill and the debate in the legislature made it very clear. They just got cold feet after all the protest.