The constitution was written to constrain the gummint.
Did you listen to POTUS Trump’s weekly address yet? He’s slamming CAL for violating the citizen’s constitutional rights with open borders and so on. So that is a state government being constrained by the Constitution.
But what about in the pre-civil rights days with whites only fountains and seating? That was decided to be unconstitutional; violated by private businesses. So it seems that definitely a private entity can violate citizens’ constitutional rights as well.