So, after a bit of digging it seems I slightly misunderstood what was causing the original issue.
In differential pair mode, the clearance check is failing on the leg-to-leg connector pads (not the legs to the adjacent non-pair pads) since they're less than 0.25 mm apart.
The fix for this issue is to ensure that the DP clearance is only imposed from trace to trace, and the normal netclass clearance is used for trace-to-pad checks. In the screenshot, it should be legal for pad 15 to be less than 0.25mm from pad 17 as long as the traces fan out to the correct distance once they leave the pads.
So, after a bit of digging it seems I slightly misunderstood what was causing the original issue.
In differential pair mode, the clearance check is failing on the leg-to-leg connector pads (not the legs to the adjacent non-pair pads) since they're less than 0.25 mm apart.
The fix for this issue is to ensure that the DP clearance is only imposed from trace to trace, and the normal netclass clearance is used for trace-to-pad checks. In the screenshot, it should be legal for pad 15 to be less than 0.25mm from pad 17 as long as the traces fan out to the correct distance once they leave the pads.