It utterly wrong but at present, religious rights trump all.
This isn't true. It's illegal to discriminate against people with protected characteristics on religious grounds when providing most services (religious services excluded).
There have been a couple of successful cases, one a Christian bakery in Northern Ireland which refused to make a gay rights cake and another a Christian B&B which refused to provide a double room to a gay couple.
The people who bring these cases are never, ever brave enough to target Muslim businesses because they fear on the one hand Muslim fundamentalist and on the left cries of 'racism', 'islamaphobe'. So Islam is effectively excluded from those laws.
Religion in general doesn't trump everything, only Islam. This is because the left wing and liberals enforce a right apex of social justice which Muslims are firmly at the top of and therefore discrimination against all other groups below them in that pyramid is tolerated.
eg my wife does not wish to shake anyone's hand. is she being rude? I don't think so. She has a right to do with her hands what she wishes, and clasping someone else's is her right to choose.
As has been said multiple times, if your wife refused to shake hands with a Muslim, a Jew or a black person it would not be okay and she would probably have been escorted from the premises and told to shove her business up her arse.
If someone wishes not to shake hands they need to not shake hands with anybody, not discriminate. Other people also have the right to think she is a rude dickhead if she chooses to shake some people's hands while ignoring others, because she would be.