In my opinion, the only thing that shouldn't be too red is people's faces, and the faces in this icon come out really nicely!
If you're using Photoshop, the best way to increase contrast without increasing saturation (and thus turning everything red) is using Gradient Maps.
Create a Gradient Map adjustment layer, choose a simple black-white gradient, and set it to Soft Light. This will make the dark colors darker and the light colors lighter - i.e. increase contrast. But unlike using Contrast adjustment, it will not make everything red, but rather desaturate it just a little bit.
Re: LIYM
In my opinion, the only thing that shouldn't be too red is people's faces, and the faces in this icon come out really nicely!
If you're using Photoshop, the best way to increase contrast without increasing saturation (and thus turning everything red) is using Gradient Maps.
Create a Gradient Map adjustment layer, choose a simple black-white gradient, and set it to Soft Light. This will make the dark colors darker and the light colors lighter - i.e. increase contrast. But unlike using Contrast adjustment, it will not make everything red, but rather desaturate it just a little bit.