Read a book in the mid 2000s about a group that was persecuted, Christians I believe, that accidentally discovered FTL travel. They built a ship and left Earth. They discovered a new planet, and filled with new plant and wildlife. However, they found they were still pursued, even after leaving Earth.
This might be James F. David's Judgment Day, published in 2005.
Kingdom of Light; The Forces of Darkness
Ira Breitling---Man of God; Manuel Crow---Lord of Darkness
Even the universe is not big enough for the both of them . . . especially when Ira Breitling is handed a divine gift---an interstellar engine that can lift humanity into the heavens. Crow---awash in riches, commanding nations, supremely powerful---swears eternal vengeance on Breitling and his Fellowship of the Faithful . . . and on all humankind.
The reign of Lucifer---prophesized as a thousand years of darkness---is about to begin. With the world falling fast under Crow's violent sway, Breitling's Fellowship---having only one choice---seizes their divine gift, their faster-than-light flight, and flees the earth. Their journey takes them beyond the distant stars to a perfect planet uncorrupted by Crow and his Kingdom of Darkness.
But even as Manuel Crow razes and racks the Earth, Revelations' scourge is not yet sated. Crows eyes the heavens, fixed on the Faithful.
Ira Breitling and the Fellowship must defend not only themselves but the soul of all humanity: A Kingdom of Light against the Forces of Darkness. Will the Fellowship prevail . . . or fall under Revelations' reign?
Let the battle begin.
I found it by searching for science fiction novel christians develop FTL to escape persecution