I don't have a stock stereo but still have a stock amp. I've never had any trouble with starting and always left my stereo on when I shut down the car, had no trouble with the stock Shaker 500 for a couple years and still no trouble with an aftermarket unit for the past 6 months.
Looking at the wiring diagram there's nothing that stands out as problematic. Granted I wouldn't expect to find anything there... the 'problem' would likely be internal to the radio or amp so the diagram provided is pretty much irrelevant. I'd need a schematic of the Shaker H/U and/or amp internals to even start looking for a possibly problematic circuit.
All I see in the provided diagram is a run of the mill basic car stereo wiring setup... Shielded aux input, antenna(s), constant +12V, switched +12V, and ground signals as inputs, speakers as outputs, and (in the Shaker's case) a couple data lines to control the function that adjusts volume based on vehicle/engine speed.
I'm not saying there *isn't* a problem with some cars (or some stereos/amps), but this is the first I've ever heard of it and never had any trouble with stock or aftermarket stereos. Any stereo will cause a SMALL drain on a battery even when the vehicle is off... that's almost necessary in order to save your presets and settings... but this drain is pretty much negligable.
If you're having trouble I'd suspect it's something other than your stereo unless you've done the tests to prove it's the stereo.. If you can, pull the head unit and amp from the vehicle and use a multimeter to measure the current that your head unit or amp are drawing while the vehicle is off. That's the only way to know for sure exactly how much power the component is using in an 'off' state.
2005 Windveil Blue GT (MT)
93H Bama tune, JLT Series 3 CAI, FRPP CMDPs, Pype bomb super system, 3.73 gears, Steeda shift bushings, Saleen short shift block
Steeda ultralite springs, Tokiko D-specs, J&M Extreme joint UCA/LCAs, PHB, C/C plates, bumpsteer kit, Steeda Q1S wheels, 2011 GT brakes, 275/40R18 Sumi HTR Ziii tires