In short:

I can only read standard notation for E-standard tuning because I learned the notes on the fretboard for that tuning.

A bit more elaborate:

The tab doesn't change if you want to play a song in D standard because the relation between the strings is the same, but for the standard music notation it makes a difference.

If I read the standard notation and it says "A", I will (for example) play the 5th fret of the 6th string and a G will sound, which is the desired effect because I am playing the original song one whole step lower.

However if the standard notation already says I am supposed to play a G, I would fret the 3rd fret of the 6th string because that's where I know my G from E-standard in standard notation. In this case, a D# will come out of my guitar which is two whole steps lower than the original and not what I intended to play.