If a warlock with the Repelling Blast eldritch invocation casts eldritch blast and hits, must the targets always be pushed back? Or can you choose not to push back the target?
You don't have to push
The wording on Repelling Blast is (emphasis mine):
When you hit a creature with eldritch blast, you can push the creature up to 10 feet away from you in a straight line.
--- Player's Handbook, p. 111
The can here functions as an optional, meaning you are free not to do it. If that word had been omitted you would have no choice, but it's there so you do.