Anti-aliasing of red text on white background

As explained in the comments, text rendering is special and has sub-pixel anti-aliasing which introduces the colours. This does not occur with other graphics primitives like lines, circles, polygons etc. just text.

ImageResize[Rasterize[Text["Hello"], RasterSize -> 16], 100, 
 Resampling -> "Nearest"]

ImageResize[
 Rasterize[Graphics[Line[{{0, 0}, {1, Sqrt[2]}}]], 
  RasterSize -> 16], 100, Resampling -> "Nearest"]

I don't know how to turn off the subpixel anti-aliasing but this work-around can turn the text into a mesh which will then render without the subpixel anti-aliasing colours appearing:

mesh = ImageMesh[
  ColorNegate@
   Rasterize[
    Graphics[
     Text[Style["Mathematica", RGBColor[0, 0, 0], Italic, 30]]], 
    RasterSize -> 1500]]

gr = Style[Graphics[{EdgeForm[None], FaceForm[Red], mesh}], 
   Antialiasing -> True] // Rasterize
colors = Flatten[ImageData[gr], 1] // DeleteDuplicates;
Graphics[MapIndexed[{RGBColor @@ #1, Disk[{8 First[#2]/10, 0}]} &, 
  colors], ImageSize -> {Automatic, 100}, Background -> Black]
Graphics[Table[{Blend[{Red, White}, x], Disk[{8 x, 0}]}, {x, 0, 1, 
   1/10}], ImageSize -> {Automatic, 100}, Background -> Black]

---

Another trick you can use is to export it as SVG then re-import it using ResourceFunction["SVGImport"]. This has the effect of breaking the text down into FilledCurve primitives which will not render with subpixel anti-aliasing:

svgtricktext = 
 ResourceFunction["SVGImport"][
  ExportString[Text[Style["Hello", Red]], "SVG"]]

---

I've been searching around and apparently there's this trick where you can set the opacity to 0.999 and it either triggers greyscale sub-pixel rendering or turns it off instead of doing RGB subpixel rendering. See here, and here

Rasterize[Style["Hello", Red, FontOpacity -> .999], RasterSize -> 32]

Another standard way:

graphicsText[x_] := ImportString[ExportString[x, "PDF"], "PDF"][[1, 1]];
gr = Graphics@ graphicsText[
   Text[Style["Mathematica", RGBColor[1, 0, 0], Italic, 30]]]
colors = Flatten[ImageData[gr, "Byte"], 1] // DeleteDuplicates;
Graphics[Table[{RGBColor @@ (colors[[x]]/255), 
   Disk[{8 Mod[x, 40]/10, -2 Floor[x/40]}]}, {x, 1, Length[colors]}], 
 ImageSize -> 400, Background -> Black]
Graphics[Table[{Blend[{Red, White}, x], Disk[{8 x, 0}]}, {x, 0, 1, 
   1/10}], ImageSize -> 400, Background -> Black]