I think for a classical guitar you need to tune down a semitone as well as standard tuning is too much tension for the neck. So I heard, dunno, don't own one.
And as for playing with out the D string.
I hate restringing all strings at once, it takes ages for it settle back and me not having to retune every hour
To be honest, as I'm only playing for myself at home, this time I'm changing on a per need basis. Right now my D string is looking in need of change, but the others ok.
Is it an electric with a Flloyd Rose?
Otherwise you might have knackered or rubbish machine heads. Acoustic's tuning doesn't drift that much IME, at least in our climate.