Grainy 2D RegionIntersection Plot: How can I make it smoother?

In addtion to Carl's answer, you can also force to rasterize the image with customized resolution. Takes longer but creates higher resolution bitmap images.

g = Show[Graphics[{Red, rDisk}], Graphics[{Blue, bDisk}], 
   Graphics[{Green, gDisk}], 
   Graphics[{Blend[{Red, Blue}, 0.5], BoundaryDiscretizeRegion[rbDisk]}], 
   Graphics[{Blend[{Red, Green}, 0.5], BoundaryDiscretizeRegion[rgDisk]}], 
   Graphics[{Blend[{Green, Blue}, 0.5], BoundaryDiscretizeRegion[gbDisk]}], 
   Graphics[{White, BoundaryDiscretizeRegion[rgbDisk]}]];

Show[
 Rasterize[g, ImageResolution -> 1000],
 ImageSize -> Medium
 ]

You can use BoundaryDiscretizeRegion instead of DiscretizeRegion to avoid the mesh lines when using Antialiasing->True:

Graphics[{
    {Red, rDisk},
    {Blue, bDisk},
    {Green, gDisk},
    Antialiasing->True,
    BoundaryDiscretizeRegion[rbDisk, MeshCellStyle->{2->Blend[{Red, Blue}]}],
    BoundaryDiscretizeRegion[rgDisk, MeshCellStyle->{2->Blend[{Red, Green}]}],
    BoundaryDiscretizeRegion[gbDisk, MeshCellStyle->{2->Blend[{Green, Blue}]}],
    BoundaryDiscretizeRegion[rgbDisk, MeshCellStyle->{2->White}]
}]

pts={AngleVector[60°],{1,0},{0,0}};

colors=Join[{r,g,b}={Red,Green,Blue},Blend[#,0.5]&/@{{r,g},{r,b},{g,b}},{White}];

regions=BoundaryDiscretizeRegion/@RegionIntersection/@Rest@Subsets[Disk/@pts];

Graphics[Thread[{EdgeForm/@colors,colors,regions}]]

or

Graphics[Thread[{colors, MeshPrimitives[#,2]&/@regions}]]

If need faster speed, I prefer use Graphics`PolygonUtils`PolygonIntersection

Manipulate[
  Graphics[{
    Thread[{{Red,Green,Blue,Yellow,Magenta,Cyan,White},
    Rest@Subsets[Polygon@CirclePoints[#,1,100.]&/@pts]
  }]/.{c_, p:{_Polygon,__}}:>{EdgeForm[c],c,Graphics`PolygonUtils`PolygonIntersection[p]}
},PlotRange->2.5,Background->Black,ImageSize->Large],
{{pts,CirclePoints[1/√3,3]},Locator}]