Here is one way to do it. I remade your T_warn1 texture as T_warn_2. You might
need another very similar texture (with a different radial 'frequency') for your
plane, so that the warning stripes there look equal in size to the cylinder's
stripes.

#declare T_warn_2 =
texture{
pigment{
    radial
    sine_wave
    frequency 16
        color_map{
            [.5 rgb 0]
            [.5 rgb <1,.7,0>]
                 }
       }
    }

#declare Thing=
difference{
sphere {0,9.05 pigment {rgb 0.1}}
sphere {0,8.55 pigment {rgb 0.1}}
cylinder{<0,-10,0>, <0,10,0> 5.01 // made in Y instead of X
  texture {T_warn_2}
  rotate 90*z
  }
plane {z,-1 hollow texture {T_warn_2 rotate 90*x}}
finish {diffuse .25}
photons {collect off}
}

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