I'm looking at getting the 2012 American Strat and am new to Strats. How do they handle alternate tunings? Does it have any problems with drop D, Open E and Open G tuning?

You probably need to adjust truss rod for proper neck curve. Is this mean for you Strat have a problem to handle tuning ?

I really just meant is there any problems with playing in different tunings on a start. I didn't think there would be but wanted to make sure.

No problem.

If you set it up as a hard-tail with the tremolo springs or block the tremolo, you should have no trouble changing tunings. If you want the tremolo to float, you will need set up the guitar for that particular tuning. I personally don't use open E as one must tune above standard pitch and this puts more strain on the guitar.

My preference for open tunings is to use a Telecaster.

Strats are rock solid. Unless you really get very radical with newly invented alternate tunings (for the life of me I don't know what it would take) you will experience nothing but solid reliability. As long as I have a good quality set of new strings on mine I can pound the living hell out of mine and they stay in tune all night. I have a bigger problem with string breakage than tuning and I have always pushed these guitars to their limits.
There is a reason Fender has been a long time leader in the business.

NBG

I use open D and open G on one of my strats for slide. No problem at all.
Depending on string gauge you might have to adjust the truss rod, that's it! But that has nothing to do with the open (or alternate) tunings, it's just a matter of string gauge.

Heavily dropped tunings might also need a truss rod adjustment due to way lower pull of the strings.

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STRATS ROCK!!! but Teles and Firebirds, too!