In the context of liberalism and rights, you can certainly establish a system of natural law based on reason instead of the existence of God. Whether or not 'reason' comes from God is an interesting ontological question, but irrelevant to political philosophy. The point is that we can derive ethics from observations on the natural world. It is an apple's nature to fall to the ground, and based on observation of cause and effect, we have described a set of laws for this phenomenon. There is nothing particularly mystical or religious about gravity.
When a government passes a law that prohibits transgender people from obtaining healthcare to treat their condition, that is a violation of their natural right to live.
There is no shortage of genocides and pogroms committed by religious groups, were they being 'nihilistic'?.
That's a stretch and regardless, what influenced the ideas of liberalism is a non-sequitur.
No one has the right to use violence against someone for being gay or transgender. Whether being gay or transgender is immoral or not is a religious question and not something politics can adequately answer.
When a government passes a law that prohibits transgender people from obtaining healthcare to treat their condition, that is a violation of their natural right to live.
There is no shortage of genocides and pogroms committed by religious groups, were they being 'nihilistic'?.