This oil will not harm the motor in So. Cal. IMO
I would be concerned with the 15W starting weight in the cold climates though. And maybe for torlerences until warm. But given the 50W top end, I doubt tolerances are an issue. The 50W is spec for the cars and it will be the same when the car is warm.
Until you drain it for the proper starting weight, (which BTW is a national avg. If they only sold GT's in Palm springs and did not care about EPA ratings they may have used a 10w to begin with. ). Let it idle longer to warm up. Once you are at operting temp it will not do any damage.
I think we are are a little paranoid about the oils. I have been selling motor oils for nearly 30 years, been to many labs and on many plant tours, dyno tests, wear tests, etc. The specs can be different in each blend, but the Mobil 1 is one of the best in the industry for an alum motor. And for the record Motorcraft does not blend any oils or chemicals. They are all private labeled something else.
Keep in mind this Motorcraft weight is odd and Ford does not use it in anything else high production. It will be gone ( not available in motorcraft) in a few years and we will all be using something else anyway. Until then, I will use the Motorcraft, with Mobil 1 being my second choice.
Don't panic...just have them order the spec stuff and change it again.