When you don't argue logically, you end up beating up on strawmen.

Here, Lindsay Beyerstein defines an argument through her eyes, then concludes bigotry.

Thune's predicting that his own party is full of bigots who would oppose a nominee on the basis of their sexual orientation. If Republicans oppose a gay nominee for being gay, knowing nothing of their stance on any issue, they thereby discredit their own standard excuses for opposing legal equality for gays and lesbians.
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By balking at the prospect of a gay nominee, the Republicans would be acknowledging what we've known all along, that their recalcitrance is not about religious freedom, or the family, or any of the usual bullshit excuses for prejudice--they just plain don't like gay people.

Open to another explanation? How about... Thune is objecting to a situation where the president considers and possibly chooses a SCOTUS nominee, based on being "the first" (or the third, even) of this group or that, and lets identity groups have overwhelming input on the selection.

"I know the administration is being pushed, but I think it would be a bridge too far right now," said GOP Chief Deputy Whip John Thune. "It seems to me this first pick is going to be a kind of important one, and my hope is that he'll play it a little more down the middle. A lot of people would react very negatively."

You can stick with the "If you object to an openly gay candidate, you're a bigot" logic, LB, and take to distributing scarlet letter "B"'s, but can you at least see how some people might prefer the next nominee not receive any artificial "bump" in the nomination process based on personal characteristics or identity group lobbying, as Thune expressly states?

Particularly if it is not necessary to a particular issue at this time to send in someone where the appearance would be they are voting their own, or an identity group issue, rather than evaluating neutrally and coming to a similar conclusion nevermind the Justice's own personal characteristics. See Iowa's state constitutional decision. It can be done, you know.
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ADDED: Sound to me like Thune was just pro-actively responding to demands like this, linked above:

So why not on gay rights? Where is our New Deal?

It is the memory of 1993's gays-in-the-military debacle (and a desire never to repeat it) that has both the president's advisers and policy advocates holding back, waiting for some magical "right time" to move boldly.

This is a bad strategy. President Obama will never have more political capital than he has now, and there will never be a better political environment to capitalize on. People are distracted by the economy and war, and they are unlikely to get stirred up by the right-wing rhetoric that has doomed efforts in the past.

Yeah, sneak it in now, while the time is opportune. People will never notice. And it's the only way to get the win anyway, right?