A few weeks ago, we noted that we don't really know how Americans feel about so-called bathroom bills, an issue that has taken hold thanks to a controversial new North Carolina law. There just hasn't been a ton of public polling on this.

Now we have a better idea. And it's not good news for supporters of what North Carolina Republicans are doing.

A CNN/ORC poll released Monday found a majority of Americans (57 percent) don't agree with bathroom bills like the one North Carolina is defending that restrict where transgender people can use the bathroom, while 38 percent do.

As usual with contentious issues, there's a partisan trend. People tend to agree with their political leaders on this:

But notice that last number. Almost half of Republicans are opposed to laws requiring transgender people to use the bathroom on their birth certificates. In fact, according to the CNN poll, Republicans are actually split 48-48 about whether to support these bills.

If Republicans are indeed split in their support for bathroom bills, it's in stark contrast to the news in recent days. In North Carolina, the epicenter of these bathroom debates, GOP  leaders are digging in their heels to defend it, betting voters will back them up in November. They just sued the federal government to try to keep it on the books. (The government counter-sued.)

Socially conservative North Carolina may be in a slightly different political situation than the rest of the nation. A recent Elon University poll showed 49 percent of all North Carolina voters agreed with the law's aim to stop cities from passing ordinances that open up bathrooms to transgender people; but that same poll showed Gov. Pat McCrory's (R) Democratic opponent with his biggest lead yet in the tight race.

This is one of those issues where it's easy to slice and dice the numbers to make your case that you are doing the popular thing. Americans' -- and particularly Republicans' -- support for bathroom bills might depend how you frame the question. As we saw in Houston in November, opponents of an LGBT non-discrimination ordinance overwhelmingly defeated it by framing the issue about bathrooms, specifically the predators who might exploit an open-door policy.

This CNN poll was more straightforward, if not a bit confusing. It asked whether people support laws requiring transgender individuals to use facilities that do not correspond to their gender identity (i.e. requiring transgender people to use the bathroom they may not normally use).

The answer may also depend on who's going to the bathroom. A CBS poll in 2014 found the exact opposite result when asking about school-aged transgender children and what bathroom they should use. Fifty-nine percent of respondents said the children should use the bathroom of the gender of their birth. Let's not forget that this bathroom bill debate is as much about adults as it is children; several recent lawsuits and flash points have centered on which locker rooms transgender students can use.

But on the whole, this poll is positive for transgender advocates. And there is more good news: Americans' support for opening up bathrooms (and Republicans' indecision) appears to be happening without one of the driving forces in the gay marriage debate -- a familiarity with the LGBT group involved. Eighty-five percent of respondents told CNN they don't have a friend or family member who is transgender.

The first major national poll on transgender adults in bathrooms would suggest the nation is leaning toward allowing them into bathrooms -- without even getting to know them first. That's pretty remarkable. As we've documented, Americans' familiarity with gay people in their personal lives was a huge contributing factor in reshaping public opinion over gay rights in favor of same-sex marriage so quickly.

Clearly, there's still a lot we don't know/a lot that isn't settled about public opinion in the bathroom debate. But the initial results look promising for LGBT advocates, who hope to convince the greater public there's no real danger to opening up their bathrooms and locker rooms to trangender people. This poll suggests Americans might be amenable to that argument.