Our FCOM says, in the limitations section:
AAA through CCC
For single channel operation during approach, the autopilot shall not remain
engaged below 50 feet AGL.
DDD through ZZZ
The autopilot must be disengaged before the airplane descends more than 50 feet below the minimum descent altitude (MDA) unless it is coupled to an ILS glide slope and localizer or in the go-around mode.
DDD through ZZZ
The Minimum Use Height (MUH) for single channel autopilot operation is defined as 158 feet AGL.
AAA through CCC are older airframes, so maybe there is different software/hardware involved.
I was told that on an autoland the newer aircraft stop making any additional drift corrections below 158' radio, ie it smacks into the runway with whatever drift it has at this point. This is why you do not always land bang on the centre line.
This would also explain why you won't want the A/P engaged below this height, since an autoland has much stricter crosswind limits than a manual landing.
Our FCOM also states that the older A/C have a 20k xwind limit for autolands, and the newer A/C only have a 15k xwind limit. The older A/C would keep adjusting drift down to 50', giving the A/C less time to drift off the centre line below this point and hence a higher xwind limit.
Could it be that the point at which the A/P stops making drift corrections is set to a lower value in the -700 (135') than the -800 (158') and hence the difference in MUH?
Ps: I have an FCOM for a company I was involved in a couple of years ago. It states 140' ARTE for the -300 and 50' ARTE for the -700 with 15 kts xwind limit for both.
Maybe this is just one of those 'pay us more money and we will give you better limits' tricks that Boeing like to play.