How can I disable the tire pressure monitoring system on my 2009 Mazda 3 so that it doesn't warn me upon starting the car and doesn't maintain a yellow warning light on the dash if it can't detect the wireless sensors?
In the United States, it is illegal to work on someone's vehicle, render TPMS non-functional, and return it to the customer. As such, no shop or dealer will ever do this for you.
It's perfectly legal for you to do it yourself.
Now that that's out of the way...
Some vehicles can have the TPMS disabled by physically removing the module and coding it out of the computer system. My 2008 BMW is this way, as its computer system was designed prior to the TPMS requirement and was sold in markets without it, and the TPMS was added on later.
From searching, I don't believe your Mazda is designed in a way for this to be possible. If that's the case, you would have to devise some kind of hardware to either trick the TPMS module, or modify the module to always report OK regardless of actual sensor state. Either way, this is probably not a worthwhile endeavor - the effort required far exceeds the benefit.