Well, a lot has already been pointed out here.
Part of the situation in the U.S. and others is the religion input and control.
For all the want of separation of church and state, the influence is extremely being felt in today's government and politics.
And that's scared me, more for the logic/illogic issues. (Who cares about facts? Seems to be the thought in government and their decision making processes anymore )

On the clothes side, we can easily apply the "women can dress in mens clothes,why can't we in women's?" logic... But again logic isn't treated so well nowadays. And logic alone won't change minds it seems.
The same thing applies with the 'reasoning' of why to CD...
_We_ may understand the difference between gender and sexuality. But the average person can't reconcile it.
(Hence the 'are you gay' assumptions). And they won't take some decent amount of time/effort to analyze / rework their own thought on it. ('Since it doesn't directly affect "me" it's much easier to just keep my old mindset'). Only if something is discovered closely relative/friend-wise might they look into it better.
The gender/sex aspect is also even a new thing to consider even by psychologists / therapists... So with the science-side a bit inexact it adds another layer.

Some mentioned other countries like Japan, the thing there I think is due to being a strong historical aspect.
CDing is thought in general to be primarily a couple forms... Gender expression, and fetish.
But there is the third form and has historically been part of Japan for some time...
Art,entertainment, as example Kabuki theater (1600's). And this theater has also had their lines of masters and masterworks.
Family names are traditionally kept strongly tied to these areas...just as a lot of varied skilled craft will have their known family names for the 'masters' of the trades.
Kabuki had its own seedy times...and shifting styles. Women played both gender roles for a time 'onna-kabuki'.
Later men took over both roles 'yarou-kabuki' and also it stabilized the theater style and legitimacy. It was _the_ thing to experience in city-life back then (going to theaters in 1600-1700s).
With all the Traditionalism that keeps as a core of Japanese culture, it's no wonder that CDing may be a bit more understood or identified there.
There's still the additional seedy fetish side...and the clubs you can go to to drink with CDing "waitresses",etc..just like you can find clubs having servers for all sorts of oddities. Clubs for drinking, cafés,etc are all over trying to be 'unusual' for attraction. But even these are handled with a great amount of professionalism..Japan is tops in the customer service side for these as well as stores. Wish this aspect spread to US...sigh... I digress tho.
Japan has also had its own religious upbringing with a more Buddhist and Shinto style which isn't as controlling or guilt-driven which may have allowed for acceptance of these things as well.

Now we have this in our way...what is the Drag shows nowadays. These are a different performer however, with the emphasis on over-the-top flamboyance, attitude, and with ties to many different art forms (comedy,pageantry,etc). Even these are limited in understanding by general population. It also is running into its own heyday recently however...thanks to popularity of Logo network, RuPaul's Drag Race (still a better "reality" show than most reality crap on TV nowadays, IMHO). But even this popularity doesn't really 'help' a standard CDer form of acceptance.

Aside from all this, I do think that there are bigger inroads being made to the knowledge of gender and transgender. It's getting more portrayal on TV, along with the GLB side of things. Also, a lot of this knowledge is learned and understood by us here thanks to the Internet.

Unfortunately, the decision makers, and leaders in the country do their own thing and don't want to deviate or change anything. (Metric's an example...I'm still annoyed how US is stubborn to not shift, I learned it in school in 70's..it's a logical system, easy to understand...then they drop it altogether and keep with the 'old ways') Things like this are keeping the country seeming more and more backwards. A lot get in office at an age that where they won't change, won't learn new things, or consider themselves above any such needs. This is a mindset across the country-and will hamper advances in any new or progressive thought. Fixed thought also is dangerous however.. When you know how people think it can make them more easily controlled or manipulated, especially by those with big resources behind them (media,corporations,lobbyists,government,etc).
Become stagnant in thought and self advancement as a nation, And you become less of a significance and more a joke in the world.

On the Arizona decisions (yay...let's head back to the 1950's thought.. ), my Facebook popped up with a lot of talk. A common pic was of one AZ pizzeria's sign they put up showing support with "We Reserve The Right To Refuse Service To Arizona Legislators" ... The problem is this won't really impact the rule makers there either. Doubt they themselves are involved with small businesses,pizzerias,Etc). If a business wants to limit their clientele by blocking LGBT folk...I guess they'll legally be able to. I'm hoping there'll be enough supporters (even non LGBT) to directly report support and loss of business to these places and maybe sometime down the line they'll learn how they've hurt themselves.

All in all, I myself am doing a _lot_ more paying attention nowadays to supportive businesses and places. If nothing else, it at least shows the owners aren't about to shoot themselves in the foot financially due to closed-mindedness. I frequent a small diner regularly Sat mornings and other workdays after work. I brought up my CDing to a waitress there and asked about issues with me going there sometime while dressed (usually I'm there after work so not dressed). She actually asked the owner about it...who said he didn't have any issues with it whatsoever. And this is from an older guy in his 60s himself. Whether it's his thought on CDing, the fact that he's known me (gone there regularly for several years now), or the thought of losing business I don't know. But it's sure too bad more people don't think this way.