My physicist father answered this (sort of) for me when I was young before his death.
The constellations also move with us as we are part of the Milky Way Galaxy which our sun is just one star in the vastness. We and those constellations *move together* which is why they haven't changed.
The one thing not mentioned in the meme is that the GALAXY is also hurling around the universe at a faster pace that the sun moves which is faster than the Earth moves.
BTW - how many of you have thought of this: The reason why jewelry chains and electric cords get tangled up when they haven't been touched is that we ARE moving through space at thousands of miles per hour. We may not feel it nor does it throw us off our feet, but it DOES effect those minor things more than we think.
Just a supposition of mine, but I think I'm correct on that.