Christianity is not known, at least among the sophisticated, for its violence. It is so peaceful that in an attempt to accuse it of violence, Sam Harris once quoted Luke 19:27, which, taken in the context of Luke 19:11-26, is clearly not a command to kill, but is in fact the end of a parable in which Jesus describes how He will judge the world at His second coming. Richard Dawkins, of all people, once said "I have mixed feelings about the decline of Christianity, in so far as Christianity might be a bulwark against something worse."
Christianity very much deserves this reputation. The Bible, which is the source of all things Christian, is chock full of commands and principles such as the one mentioned in the above image. Christianity is supposed to be full of the persecuted (1 Peter 4:16), but never the persecutor. Unfortunately, Catholicism didn't get the memo. Despite claiming to be able to trace its origin back to Jesus, and that its authority comes from Him, Catholicism is not known for being historically peaceful.
To clarify, the dates in the meme are not technically accurate. Heretic burning was not standard practice in 1000 A.D.* However, Catholicism did persecute dissenting voices for centuries, right up until the Reformation. Burning is the most famous punishment doled out on "heretics", mostly because of how brutal it was.
One of those burned at the stake was William Tyndale, who certainly was not a heretic. His explicit goal was to cause the boy that plows the field to know the scriptures better than Bishop John Bell, and so he committed to translating the Bible into the language of the common man. That hardly sounds like heresy to me, unlike the belief of the aforementioned Bishop John Bell that it is "better to be without God's laws than the Pope's". But it was Tyndale, rather than Bell, who was burned at the stake while crying "Lord, open the eyes of the King".
But the issue is not who was right and who was wrong. It is an abomination that Tyndale was burned for his commitment to the word of God, but Biblically speaking, it is an abomination that he could have been burned at all. Jesus gave some pretty clear instructions to His missionaries: If a house or city rejects the Gospel, leave.
Speaking as a Christian, I find the idea of heretic burning repugnant. I am literally surrounded by people with whom I disagree on a regular basis. Even some of my own family are unbelievers. I have studied with unbelievers, I have worked alongside unbelievers, I have even dated unbelievers (which isn't a practice I endorse, but is nevertheless something I have done), and yet at no point in my life have I wished it was even permissible to do violence to one of them in the name of Jesus.
I don't claim to be the perfect apologist. I've lost my temper with those with whom I disagree, even to the point where I have sworn at them. Cards on the table, I'm a fallible, sinful human being, and so while the word of God says to give reason for my hope with gentleness and respect, I confess I am often guilty of flipping out at particularly irritating unbelievers. But as much of a failure as I am, I will never endorse such vulgarity. And indeed, I at least manage to draw the line at vulgarity. It's one thing to swear at a man who threatened to shoot me, it's another thing to tie someone to a stake and set them on fire.
Under the approval of Pope Sixtus IV, the Spanish Inquisition was set up in 1478. This is by far the most brutal of the inquisitions, killing more than 30,000 people. Think about that: the so-called representative of Christ on earth directly approved the political persecution of Jews and Christians for daring to disagree with the Catholic faith. Unlike the exaggerated 1000 A.D. in the meme, 1780 A.D. is no exaggeration. In 1781, María de los Dolores López became the last heretic to be burned by the Spanish Inquisition.
Unlike the aforementioned Tyndale, López genuinely was a heretic. She made a number of outrageous claims, including allegedly having visited Heaven, had sex with Mary and married Jesus, who had informed her that she would die a martyr. And yet, the Bible sets forward no precedent for her execution. The solution, according to the Bible, is to sufficiently rebuke her, and if she refused the rebuke, to disfellowship her, treating her as any other believer. But the Spanish Inquisition, an officially sanctioned Catholic disciplinary office at the time, deemed her worthy of death.
Catholicism's history is stained with the blood of heretics and martyrs alike. In the modern day, it is relatively tame, but historically speaking, it took the Reformation to end the bloodshed. The violence of Catholicism, particularly against Christians, shows that it cannot actually be Christian. I strongly advise all Catholics to face the history of your Church head on, and realise that although Jesus will not authorise His Church to punish heretics, He will eventually do so Himself. Do not be numbered among them when He calls you to His judgement seat.
*Though not technically accurate, the meme was not intended to be deliberately misleading. The first notable heretic to be burned by Catholics, Ramihrdus of Cambrai, was burned around 1076/7, and so the meme does get the point across.