If she’s going to discriminate against which customers she serves, she should lose her job. If she doesn’t want to touch men who aren’t related to her then that’s her choice, but when this is incompatible with the duties of her job, she needs to decide which one is more important to her.
If she were the only business employee, then your position is near ineluctable. This is a scenario, however, in which her belief can be accommodated by the business while the business can still offer services.
If I’m not mistaken, Canada does have a law prohibiting discrimination in employment on the basis of religion and religious beliefs. Canadian law is not my sandbox. However, it would be interesting to know whether Canadian law has a balancing approach between the law prohibiting not hiring her to perform waxes on the basis of her religious, and reasonably accommodating her religious belief as a hired waxer, and justifiably not hiring her as a waxer because her religious belief would be an undue burden to the business, the latter justifying discrimination in employment on the basis of religion/religious belief.
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Yes, and the business was accommodating that in 99 out of 100 cases, as I stated. When you get to that 1 out of 100 cases, however, someone needs to lose out. The person who loses should never be the customer, however, since their right to receive services absent discrimination should be the thing that wins. If you have two cake makers in a shop, the anti-gay bigot can avoid making cakes for same sex weddings all he wants until the other guy doesn't show up when such a couple comes in and then the cake shop finds itself in a legal situation.
If you can't perform all the duties required of you in a job, you should not keep that job.