I have an issue with how different types of graphics are rendered alone versus in combination. If I render a simple circle like so:

Show[Graphics[{Thickness[0.01], Circle[{0, 0}, 0.8]}]]

I get a nicely rendered circle:

However, if I combine this with a slightly more fancy object like so:

Show[Graphics[{Thickness[0.01], Circle[{0, 0}, 0.8]}], 
 ParametricPlot[{Cos[t], Sin[t]}, {t, 0, 2 Pi}, 
  PlotStyle -> Directive[Thickness[0.01]], Axes -> False, 
  Frame -> False, ColorFunctionScaling -> False, 
  ColorFunction -> (Hue[0.1184738955823293, 
      0.9378531073446328, ((1. - Sin[#3 + Pi])/2.)^0.7] &)]]

I get this:

in other words, some fairly crudely rendered, pixelated objects. How can I fix this?

P.S.: I have found a reference to a similar issue here which is somewhat disheartening. If this issue still exists (the post I just referenced is almost ten years old) then we may be out of luck: Use of Colorfunction may ruin rendering quality of all graphics nearby.