Both parties largely see the constitution as something they need to get around, and have largely (with full support of the courts) inverted the meaning of the constitution to be not a limit on government power, but a limit on individual rights
In your example where Democrats support the 4th amendment, what except if a random person says you are armed then the 4th goes out the window, except if you are deemed to be rich then the 4th goes out the window, except if you have the "Wrong" opinions then the 4th goes out the windows
Democrats like Republicans only support the 4th, and every other amendment to the point where it supports their narrative and desire for power, the second the constitution is deemed to stand in the way of their power well it is document that should be ignored "for the greater good"