If you're rooted, you can grab an app called Autostarts from the market and it'll give you complete control over this... It basically gives you a list of several triggers on the phones and the apps that are currently associated with each.
I haven't tried it on my EVO 3D yet, but it was a god send on my EVO 4G after I started using the Amazon Cloud Player/Store. I wanted to keep using the stock HTC player (and it's lockscreen shortcut/display) as my daily player, but whenever I hit play on my Bluetooth remote in the car it'd bring up the Amazon player. With Autostarts I was able to stop that and whenever I hit play the stock player would start playing instead. However if I paused and opened another player (Amazon, Pandora) I could still control those w/BT keys as well.
If you're not rooted you're probably SOL, sorry. As far as the act of auto-playing itself, that's triggered by the car... My mother's Acura RDX does the same thing, there's no play button on the stereo anywhere so whenever you switch to CD or BT it just starts playing that source. Really threw me off at first, particularly with BT because even though it sends a play command to the phone when you switch it's not really instantaneous so you don't know what's going on. I'm not sure you'll be able to stop that from happening w/Autostarts (at 'least not w/o disabling remote BT controls entirely), but at the very 'least you'll be able to control which app has priority.
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