Almost certainly he would use natural products where-ever possible, things such as white vinegar as a general cleaner are far safer and friendlier to the environment than the harsh concentrated chemicals of most cleaning products. It has hundreds of uses around house as you can see in the below link. I would think that for things where you couldn't use a natural alternative, such as laundry and dish washing, he would use an eco-friendly product.
http://www.vinegartips.com/scripts/pageViewSec.asp?id=7
Another alternative I think MacGyver might use is a steam based cleaner. These work by pumping steam through a cloth covered cleaning head. The heat from the steam breaks down and loosens dirt and grease and kills bacteria and the cloth picks up and holds it all making cleaning as simple as wiping the cleaning head over the surface with no chemicals being used.
Even things like vacuum cleaners have had me thinking from the MacGyver angle. What would he look for in a vacuum cleaner. My guess would be the best clean for the least amount of electricity. This would mean probably an upright vacuum as they are considered more efficient than the canister models because the suction is right next to the carpet (instead of at the end of a long tube) and therefore at its strongest and usually employ a rotating brushroll or beater bar, which removes dirt through a combination of sweeping and vibration meaning a quicker clean and so less electricity being used.
I guess it comes down to thinking about what impacts your current cleaning methods have on the environment and how you can reduce the impact without reducing the results.
I do know that for those of us who still use 'wind power' for drying ..... the evidence in and around the backyard is more than obvious. 
