Exercise of religious freedom must not hurt others
Respecting the rights of the religious is important, but only insofar as those rights don't involve 3rd party harm.
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Religious freedom is also the bedrock of this particular argument. More specifically, how we aim to balance it with the competing right to non-discrimination of LGBT individuals.
Many rights are circumscribed when they are in opposition to another competing right. We see this when we balance the right to bear arms and the right to life; the right to privacy and the right of others to safety. Few rights are absolute and override all else. The general rule of thumb we apply to such rights is that their exercise depends on whether or not they cause harm to others. So too with the right to religious freedom - it is acceptable only when it does not harm others. This is the general principle that allows us to live in a society that is increasingly diverse and must become increasingly tolerant. There are multiple way in which the refusal of service harms LGBT individuals. The first is the emotional strain of being turned away again and again from establishments for reasons beyond their control. The second is that they may not be able to access the service if they are repeatedly turned away by all the providers in their region. This is particularly important if we consider the fact that this case may not be limited to same-sex weddings, but rather to the greater question of whether it is permissible to refuse service to a person specifically because of their sexual orientation. If any business can refuse a service to customers because they are LGBT, this puts a significant constraint on the lives of LGBT individuals.
We value rights only insofar as they do not harm others In this case, the right to religious freedom harms the rights of LGBT individual to non-discrimination and access to services Therefore, religious freedom must be suspended to prevent harm to others.