It's not really a gray area. The Civil Rights Act explicitly prohibits discrimination against protected class by most businesses that are open to the public, like stores, restaurants, bars, and hotels.

If you're not a part of a protected class, or your particular business is not covered by the Civil Rights Act, then you are free to discriminate.

So to take your example, if a bar said "Irish not welcome here" then they would absolutely be violating the law.

The main change recently is that certain businesses that produce original expression, such as web designers, can no longer be covered by the Civil Rights Act because the court thought this would conflict with the First Amendment.