Don't confuse 4/3 and micro 4/3. The sensor sizes are the same but there hasn't been an updated 4/3 DSLR with a modern sensor. On the other hand, virtually every micro 4/3 camera these days are using the latest generation sensor. Much better than before but you have to be realistic. It is still 1/4 the size of a full frame sensor after all.
Anyways, An E-M1 with 12-40/2.8 and 40-150/2.8 + TC will get you 24-300mm equivalent FOV at 2.8 (light gathering) and 300-420mm @f4 (light gathering). This kit should be roughly 2kg if I remember my figures correctly.
You'' want to look into the upcoming Olympus 300/4 that gets you 600mm equivalent FOV. F4 light gathering capabilities but f8 like DOF on m43. But to honest, at these sort of focal lengths you really don't need a very large aperture to throw things out of focus in the background.
One advantage to mirrorless cameras are that, they are mirrorless. And hence no mirror slap. So you should be able to shoot quieter on the golf course. Of course you could use live view on DSLR to match this ability. But some mirrorless models eg. Nikon V3 can be completely silent using the electronic shutter so you don't disturb the golfer.