So religious liberty should trump all other rights?
Pretty much, unless it involves actual, tangible harm to another. Hurt feelings don't count. There is no right to never have your feelings hurt.
The first reason religion needs to trump almost all else is that religion, by its nature, cannot be proven. So the only way to fairly apply religious liberty is to presumptively accept that whatever people say they believe is what they believe, even if it's bizarre, absurd, and makes no sense to anyone except the believer.
But that shouldn't be a problem nowadays. After all, we're expected to accept that boys are girls and girls are boys just because they say they are, so there's good precedent for presumptive acceptance of absurdity as truth.
The second reason is that religion is one of the few things that can compete with government for the sway it can exercise over people, and we need something to compete with government. We also need that "something" to be free of government influence and beyond its control.
That's why despotic governments throughout history have either tried to suppress religion (for example, the USSR, its satellites, Red China, and North Korea), or established state religions (for example, the entire Muslim Middle East). Despots don't want competition for the hearts and minds of the people. It's also why an estimated 10,000 to 15,000 Catholic priests, brothers, and sisters were murdered in Nazi Germany during the Holocaust.
So whether or not you believe in a religion, the evidence is pretty clear that we need religion (or at least freedom of religion) to serve as a bulwark against despotism. Even the despots themselves know this, which is why they either suppress religion or try to control it.
For example, none other than Joe Stalin -- no great friend of religion -- revived the Russian Orthodox Church after the Nazis invaded Russia in 1941, hoping that it would spur patriotism and lend the legitimacy that only religion can provide to the war against the Nazis. As powerful as Stalin was, he knew that the church was more so -- even after having been decimated as a result of decades of persecution by the Communist regime.
Rich