Hi Will. I generally like to make sure that the lowest note sounding on the guitar is the same as what the bass player is playing. So dropping the E string to D would come in handy when the D is in the bass. Similarly, I would thumb (or an pointer finger) an F# if that note was in the bass, like for a D/F# or G/F# for example. Regarding playing the open E string when you’re playing an A chord, I would usually only do that if the E was in the bass. If it’s not, and the chord is supposed to be a straight “A”, then I wouldn’t want to hit the E string – so that the lowest note sounding on the guitar would be the A string. Doing this keeps the bass line clear and un-muddied, and keeps the bass player happy that you’re not messing with the progression.
Worthily Magnify 
What about tuning to drop D, or thumbing an F#? I didn’t think letting it ring during an A chord was a big deal
Hi Will. I generally like to make sure that the lowest note sounding on the guitar is the same as what the bass player is playing. So dropping the E string to D would come in handy when the D is in the bass. Similarly, I would thumb (or an pointer finger) an F# if that note was in the bass, like for a D/F# or G/F# for example. Regarding playing the open E string when you’re playing an A chord, I would usually only do that if the E was in the bass. If it’s not, and the chord is supposed to be a straight “A”, then I wouldn’t want to hit the E string – so that the lowest note sounding on the guitar would be the A string. Doing this keeps the bass line clear and un-muddied, and keeps the bass player happy that you’re not messing with the progression.