The simple answer is no. Under the discrimination laws in Jersey, businesses cannot refuse to provide a service to someone with a protected characteristic (i.e. race, sexual orientation) because of religious, political or moral beliefs. The only exception is a recognised religious body such as the Church of England, and even they are limited.
A recent example is the Northern Irish case where a baker, who was Christian, refused to make a cake with the slogan "Support Gay Marriage." It was held that this was unlawful under their discrimination laws. Jersey's discrimination laws are similar to Northern Ireland's and so this case is relevant.
Someone who decides to engage in a business is carrying out a commercial enterprise, and is not able to refuse a service because of their personal religious, political or moral beliefs. This is not because that belief is being disregarded, but because the business seeks to distinguish between those who will receive its service and those who will not on a basis that has been expressly prohibited in Jersey.
The States of Jersey are currently inviting comments on whether to bring in a "conscience clause," which would allow businesses to refuse to provide a service if it contravened a personal belief. The UK has not been able to implement a similar clause and so it would be interesting if Jersey was able to lead the way in finding a balance between protecting people from discrimination in a way that does not ignore someone's religious beliefs.