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Is it feasible to stain a guitar's back and sides (Guild F-2512) that is made new with a natural finish?

You would have to strip the existing finish down to bare wood, apply your stain, then apply your finish of choice.

It's possible, sure, but it would be really hard to get good results. Really not recommended.

To make sure I understand your question:

1. You have a Guild F-2512 that has a natural finish;
2. You want to stain i t.

Well...it's certainly possible, to some degree. It depends a lot on what result you will consider acceptable, and the result will depend in large measure who does it. I'm sure some people here could do a fantastic job. Then there are the not-so-skilled or experienced, like me, who might make it look pretty good from twenty feet away.
It's almost certainly finished with nitrocellulose lacquer. I have no experience with using that. Hopefully some of the more knowledgeable folks will be able to give you a more definitive answer.

I suggest you enjoy the finish you paid for - - - these are inexpensive instruments and a refinish would cost more than the instrument. And a DIY attempt at stain and refinish would bring the instrument's value, including trade-in, to zero.