Part of the divide is over what those truths are, what you mean by truth, and who gets to decide what those truths are.
One of the foundations of liberalism is freedom of religion, and in the US that is defined as a separation between church and state. This is why liberals shy away from injecting religion into politics because it goes against the very liberal ideals that the US was founded on. In addition, I am sure Christians would uncomfortable with a Muslim political party that strove "to educate in truth and in righteousness". You don't have to search far on the interwebs to find conservative sites warning about Muslims trying to force Sharia law into the US.
Liberals are just fine with non-political groups "training towards righteousness". Where it gets problematic is that wall of separation between church and state. Also, liberals would be just fine with an imposed secular morality that is based on basic moral concepts shared by religious and non-religious people. We also have to keep in mind that secular doesn't mean anti-religious, only that we leave religion out of our politics and use non-religious arguments to justify our laws. If the only reason for passing a law is "because the Bible says so", then that isn't a law that liberals are likely to support.