Religious liberties is a campaign slogan used to convince morons that a candidate is on their side. The reality is that these candidates do not care about anyone's religion, much less their religious rights.
But I'm getting ahead of myself, religious rights are not allowed to be infringed on by the government, that's the current law. The part religious people often ignore is "by the government," especially those defending Kim Davis.
When you are a government official you are bound by the laws that the government is bound by when acting in that capacity. So this is what really happened.
The SCOTUS had ruled that marriage bans based on lifestyle were illegal, based on the law which demands the government not base any laws on personal choices. This means that gay marriage had to be recognized by the entire government.
Kim Davis, hired to issue marriage licenses, working as a government official had denied issuing said licenses, she failed to do the job for which she was being paid to do. Being unable to fire an elected official, the state government that she represents decided to give her an option, quit or be jailed.
Quitting would mean she no longer collected a tax funded paycheck, but being jailed meant she continue to collect the paycheck and become famous as a fake martyr. She chose jail, the religious nuts treated her as a martyr, she is still getting paid from taxes, she won.
Yes, Kim Davis did all of this for money, not surprising.