Is it a sin to own Protestant Bibles, and can their translations be trusted?

I would not go so far as to say that. Their biggest problem is that they cut the seven deuterocanonical books from the Old Testament, but their translators know the original languages, and some Protestant translations are as good as or better than some Catholic ones, because looked at academically, translation is a matter of who understands Hebrew and Greek best, whether he is Protestant, Catholic, Jewish, or Muslim. Take the liberal German scholar Rudolf Bultmann, who had no axe to grind: exegeting John 6 honestly, he said it plainly teaches the Eucharist, the bread becoming Jesus's body and blood, and those who do not eat it are condemned, so even a non-Catholic reached the Catholic conclusion. Other gifted men go off the tracks, like Karl Barth, who wrote eight exquisite volumes yet, influenced by evolution, denied original sin. So the purest translation takes the text for what it says without bias, and that can come from a Protestant, a Jew, a Muslim, or a Catholic, depending on the man doing the translating.