Is it ever okay to do this? I'll leave it up to you to decide. Did America's Founders do this? I assert, yes. Ted Kennedy did something very similar to what America's Founders and the theologians they followed did. Kennedy spoke on behalf of the Senate Floor and argued in favor of hate crimes laws that protect sexual orientation at the Federal level and invoked Leviticus. He (obviously) quoted only parts of Leviticus and ignored other parts.
Leviticus 25:10 features prominently near the top of the Liberty Bell: “Proclaim liberty throughout all the land, unto the inhabitants thereof.”
America’s Whig Founders obviously didn't quote Leviticus in favor of sexual orientation rights like Senator Kennedy, but they did blatantly rip parts of it out of context, distorted its meaning to support their Whig-republican agenda. The Founders meant "political liberty" as it related to republican self government. And Leviticus 25:10, indeed every time the Bible mentions "liberty," refers to spiritual liberty, freedom from sin or sin's consequences, and not political liberty which was a wholly a-biblical concept. As Tory minister Jonathan Boucher put it, "The word liberty, as meaning civil liberty, does not, I believe, occur in all the Scriptures." From a strict orthodox biblical perspective on this specific issue Boucher and the Tories were right, America's Whig Founders were wrong.
America's Founders and some of the pro-republican ministers (the most notable of whom weren’t orthodox Christians, like Jonathan Mayhew) quoted parts of the Bible that CLEARLY relate to spiritual liberty (or freedom from sin) in favor of the wholly a-biblical notion of political liberty. And indeed, perhaps, America's Founders and the theologians they followed like Mayhew felt free to use unorthodox, cafeteria like hermeneutics (like Ted Kennedy) because they themselves were not orthodox Christians who believed the Bible the infallible Word of God but theological unitarians who believed the Bible partially inspired.
But the bottom line is the traditional orthodox biblical meaning of “proclaim liberty throughout the land” has nothing to do with what America’s Founders were trying to accomplish from 1776-1800, anymore than Leviticus has anything to do with Ted Kennedy’s invocation of it in favor of federal hate crimes legislation that protects sexual orientation.