The screen color is retrieved here: 

vec3 screen_col = texture(TEXTURE, screen_sample_uv).rgb

After this, you could check if that color is red by some metric (ex. if red value is 4 times greater than blue/green). Then when you apply the final color step, use a red gradient texture if the screen color is red

if( <screen_col is red> )
final_col = texture(u_color_tex_reds, vec2(col_sample, 0.5)).rgb;

Something like that should work

Oh I found the answer in someone else's reply on the godot shader's website

To make work with Godot 4 change line 9 from

uniform sampler2D u_dither_tex; 

to

uniform sampler2D u_dither_tex : repeat_enable;