So it does indeed work with 4.0.2. Let me see if i can get to the bottom of this 
Here is what I found out so far...
If I put the memcard created and saved by the latest INTO 4.0.2, it sees no saves in game.
If I put the memcard created by 4.0.2 INTO the latest, then it works fine...
Also any saves after this work like a champ so perhaps it is the creation of the initial memcard that is messed up?
Working versions:
4.0.2
3806
5022
5603
Hmmm, the latest works fine for Mario Golf Toadstool Tour...perhaps it is an issue with the game needing a system save file?
Final Edit:
I guess my download of Dolphin was corrupt? After all that testing and finding no issues, I redownloaded the latest and now I dont have the issue...so...I guess...I am stupid
Here is what I found out so far...
If I put the memcard created and saved by the latest INTO 4.0.2, it sees no saves in game.
If I put the memcard created by 4.0.2 INTO the latest, then it works fine...
Also any saves after this work like a champ so perhaps it is the creation of the initial memcard that is messed up?
Working versions:
4.0.2
3806
5022
5603
Hmmm, the latest works fine for Mario Golf Toadstool Tour...perhaps it is an issue with the game needing a system save file?
Final Edit:
I guess my download of Dolphin was corrupt? After all that testing and finding no issues, I redownloaded the latest and now I dont have the issue...so...I guess...I am stupid
i5-8600K @ 4.5 GHz
GeForce GTX 1080 SC2
ASRock Z370 Taichi LGA 1151
CORSAIR Vengeance LPX 16GB 2400 DDR4
SAMSUNG 970 EVO M.2 500GB PCIe SSD
Indigo Xtreme TIM
Phanteks Pro ES614P Black Steel Case
EVGA SuperNOVA 750W PSU
Windows 10 64-bit
GeForce GTX 1080 SC2
ASRock Z370 Taichi LGA 1151
CORSAIR Vengeance LPX 16GB 2400 DDR4
SAMSUNG 970 EVO M.2 500GB PCIe SSD
Indigo Xtreme TIM
Phanteks Pro ES614P Black Steel Case
EVGA SuperNOVA 750W PSU
Windows 10 64-bit