When viewing an object in object mode with viewport shading set to material:
Is there a way to change this red reflection to a different color?
I'm using principled shader in blender 2.79
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These reflections are caused by the default Blender viewport OpenGL shading lights, which apparently becomes more visible in materias using the Principled BSDF Shader.
You can change this from the User Preferences > System tab under Solid OpenGL Lights.
The offending color is by default most likely the last Specular entry. Change it to whatever color you like, make sure you Save User Settings if you want it set by default.