Zero major issues auto docking with my asp, and i just got done grinding 322 missions for faction rank - half or more landing at outposts.
A very few, i'd say 2% or less minor bumps but only specific to outposts AND me manually boosting before SDC enabling.
1 every 50 landings on outposts, if i manually boost just before contacting for dock permission - seems in very small to ~2% of the time, confuses the SDC and i hit the pad at moderate speed, basically a soft crash landing. No dmg with shields, minor hull dmg without
but only way i can replicate the error is if i really boost hard , right before engaging SDC that then does the usual boost-boost to close range
so overall, zero problems ever with my cargo ships at big stations, and low percent - minor bump off pad on outposts