This is basically the "No True Scotsman" move, which isn't an argument but an attempt to distract your attention. Since there are numerous passages in the Torah and Prophets where Yahweh commands Israel to murder all the pagans and their livestock and burn their cities to the ground, it seems that "loving thy neighbor and even thy enemy" is perfectly compatible with mass slaughter. One Christian told me that God had to do this, because otherwise the Israelites would have enslaved the people, and that would be worse than killing them. He forgot that in other Canaanite cities, Yahweh commanded that at least some of the inhabitants (virgin females, usually) should be enslaved.
In the New Testament, love is evidently compatible with Jesus verbally attacking his fellow Jews and condemning people to eternal torture if they didn't meet his impossibly high standards of attitude and conduct. Sometimes he just insulted people at random, like the pagan Syrophoenician woman he called a dog when she begged him to heal her sick daughter. Yahweh and Jesus can hardly be dismissed as marginal figures, bad apples who make Judaism and Christianity look bad.
It's ironic to see this meme citing Paul, who wrote, or rather dictated, the letter to the Romans, because Paul is a popular whipping boy for liberal and especially for gay Christians. Even a lot of self-identified non-Christians denounce Paul as the original betrayer, worse than Judas, who replaced Christ's simple and beautiful message of Love with a bunch of Jewish stuff. In any case, Paul talked pretty sometimes, just as Jesus did sometimes, but he could also be harsh when his congregations got out of line or he had to contend with other Christian missionaries whose teachings conflicted with his. Love, for Paul, must therefore be compatible with sayings like
You suffered from your own people the same things those churches suffered from the Jews who killed the Lord Jesus and the prophets and also drove us out. They displease God and are hostile to everyone in their effort to keep us from speaking to the Gentiles so that they may be saved. In this way they always heap up their sins to the limit. The wrath of God has come upon them at last.Love must also be compatible with the outpourings of rage I've seen from LGBT and allied people in response to the antigay Christians who denounced last week's Supreme Court decision on same-sex marriage, since their reactions generally accuse their opponents of "hate." This implies that the pro-gay side is motivated by "love." They could've fooled me.
Is "hate" compatible with authentic religion? I'm an atheist; it's not for me to say, and I really don't have an opinion on the matter. Personally I think that hate is as valid as love, and I'm not the first person who's noticed that they aren't that far apart, whether in sacred or secular domains. It seems obvious to me that not only ordinary believers but the great exemplars of religions have spoken and behaved hatefully as often as they have spoken and believed lovingly. If you take the Bible as an account of the wishes of Yahweh, which seems reasonable to me, there's no question that he often wanted large numbers of people to be butchered to appease his wrath; if you don't take the Bible as an account of the wishes of Yahweh, I don't know what evidence there is that he disapproves of slaughtering whole populations who worship the wrong gods, or worship the putatively right one in the wrong way. The popular way out of this problem is to insist that when Yahweh commanded mass killing, when he erupted into paroxysms of misogynist abuse, when Jesus threatened the mass of humanity with eternal punishment, they did so in a spirit of Love that is so far above the pathetic human standard that we can only contemplate it with awe and humble self-abasement at our failure to be as holy as they. It's impossible to prove such claims wrong, since they have nothing to do with reason; but one can still reject them. One can still say, with Huck Finn: All right then, I'll go to Hell.
As far as I've ever seen, though, no religious teacher, ancient or contemporary, explicitly preaches Hate. They all insist that they are preaching Love. Even the Westboro Baptist Church, as far as I know, claims that God hates fags; if they also hate us, it's because they must stand with God, and hate what he hates. And why not? But most believers call their teachings Love. The liberal gay and pro-gay allies who expressed their eagerness to see a Texas preacher immolate himself in protest of same-sex marriage being legalized, don't seem to have thought they were preaching hate; they thought he was the hater, so by the simple process of elimination they must be full of Love. It doesn't seem that he actually said he would do it -- like a true War Wimp for Jesus, he said that other people should put their lives on the line for traditional marriage -- but who cares about facts? There's no time to be accurate, honest, or rational! We're fighting a war against Hate here! Ironically, the only Christian minister who's actually set himself on fire in response to this issue was a pro-gay Methodist who burned himself to death in 2014, leaving a suicide note explaining that "the self-immolation was an attempt to die a martyr for the black and LGBT communities."
Arguing about whether hate is compatible with true religion (or true atheism, for that matter) seems to me a distraction from more important questions. It's so much easier, though, than thinking.
But back to the meme that set me off. I know it's no fun to have other people tell you that you're going to Hell, or that you're a bad person because of your sexual tastes and practices, and if you're unlucky enough to be isolated in a hostile community, it can be very unpleasant. People who've been wounded emotionally by such communities can be excused if they have trouble discussing these issues rationally, but they're in no position to condemn others for irrationality -- especially if their responses consist mainly of "Oh yeah? Well, you're going to Hell!" Which they mostly do. See you in Hell, folks!