When did you last dock? NPC now follow the green-side rule, so does the docking computer. Exceptions: T-9, Anaconda and Clipper go center, no other ship will fit at the same time.
Anything that can land on a small pad can easily fit past. Most of the small ships can rotate 90 degrees to the slot and use the narrow channel at the ends.
I actually exited past a T-9 once in a Python without a scratch by rotating at 45 degrees and placing one side well into the narrow channel. I wouldn't recommend it as a standard practice, but I can confirm that it can be done. I have had another commander tell me that 3 Anacondas can use the slot at the same time, but I've never done that, Two Anacondas is never an issue.
The slot is way bigger than you think.