First of all, the repetition of the word "himself" makes this phrase rhetorically powerful. If you have ever seen the movie "Liar Liar," you will remember the scene where Jim Carrey is in the bathroom beating himself up--punching himself, throwing himself against the wall, and smashing his own head with the toilet seat. That is the sort of picture of God that this phrase paints. To zero in on what might be the lynchpin of this phrase, I think the real power lies in the words "to himself." If it simply said "God sacrificed himself to save us from himself," it would still throw some people for a loop, but it wouldn't sound quite as ridiculous. Adding "to himself" suggests a person being sacrificed to the same person. According to the meme, that is what Christians believe. I agree that this would be wrong. In fact, this notion, coming from Sabellianism, Patripassianism, and/or Modalism, has been refuted by orthodox Christians dating back to the 2nd century and was officially condemned as heresy at the council of Nicaea. Thus, what the meme suggests is actually a misrepresentation of the Christian view. Christians are trinitarian monotheists. That is, they believe that there is one God that exists in three distinct persons. Thus, if the Son is sacrificed to the Father, it is incorrect to say that one person is sacrificing himself to himself. But pressing this point is likely to get us into a more theologically precise discussion than is necessary to demonstrate the error of this objection. It is actually a lot simpler than that.
Consider this alternate phrase: "The idea of the bank paying the bank to save me from the debt I owe to the bank is too much for any rational person to believe." Is that really so ridiculous? Of course not. Why? Because it is simply a statement of the way things are. In order for the folks at the bank to forgive a debt that is owed, they must pay the debt themselves. In the same way, in order for God to forgive the sins of all who would trust in Christ, He took the punishment for sin in the person of Jesus Christ. If you think about it, that is how forgiveness always works. The person who has been offended absorbs the debt rather than demanding it of the offender. Otherwise, the wrong remains unforgiven. The only other alternatives would not be in keeping with God's perfectly just nature. He could either simply ignore the sin, or punish a scapegoat. Ironically, many critics of Christianity often assume that the latter (scapegoating) is what happened with Jesus and they rightly cry injustice. And that is one reason why the deity of Jesus of Nazareth is so important. If James punches Larry in the face, Larry is the only one who can forgive James. Tom can't step in and say "I forgive you," because he is not the one who has been wronged. Of course, in this instance, in order for Larry to offer forgiveness, he must simply absorb the pain and forgo inflicting pain on James. In a very real sense, he is taking the punishment that James deserves. If you have ever been seriously wronged, you know how painful it can be to not react negatively in response. It is a type of death--a sacrifice of one's self. With that understood, the objection "God sacrificed himself to himself in order to save us from himself" is not so daunting. In fact, you could simply respond by asking "How is that different from how forgiveness normally works?"*
*There will be those who say "I understand that, but what really bothers me is that God would have to do it in such a gruesome way--by crucifixion. Doesn't that make God seem like a bloodthirsty dictator?" The answer is no. It wasn't the quantity of blood spilled, but the quality of the sacrifice that really matters. However, it would not have taken much resolve or obedience to God for Jesus to take a lethal injection. The quality of the sacrifice is magnified through the quantity of suffering. Furthermore, if God is the one offended, then he is the one who determines what sort of payment He will accept to settle the debt.