Are conservatives generally better-looking than liberals are?

It's true. The effect isn't as pronounced as the fact that liberals are more intelligent on average, but studies have shown a slight edge in favor of conservatives on this matter.

It's well-known that having had an easier life increases the odds of becoming a conservative and the thinking is that being better looking sufficiently caters to having a better life so as to produce a tangible disparity here.

"The idea is that the weaker man can relate more on an empathetic level to the plights of the world and thus go liberal."

This isn't true, though, especially as we're talking about women here too. The studies test the intelligence of people as small children, before their intelligence has had a chance to affect their lives much. Then they check in with them as adults and see how they ended up leaning. The genius and near-genius children overwhelmingly go hard left and the particularly dull children are especially likely to be not just conservative but very socially conservative, as in homophobic, etc. Most people are of course pretty close to average but the edge in terms of intelligence is indeed with the left.

The thinking is actually that diminished cognitive ability in general translates to lower cognitive empathy and the duller children are thus less able to process the plights of others.

At any rate, both things are true, albeit to different degrees; on average, liberals are more intelligent, and on average, conservatives are better looking.

All that said, there are still rarer conservative geniuses, liberal morons, conservative trolls, and liberal Greek gods and goddesses.

Got to say though, taking one look at a Trump rally makes it rather hard to buy, but then they're a different breed altogether.

Yeah but inteligence does not equal physical attractiveness.