My theory on this continuity issue was that in the original timeline Xavier was still on the serum Hank created. Since the events of 'Day's of Future Past’ didn't originally occur, Xavier's reunion with Magneto would of been different. I imagine they didn't finally reconnect till much later in history and by then Magneto had escaped/been freed/released from the Pentagon prison and the anger Charles had for him was now in the past which is why they were teaming up again to find new mutants.
Fast forward to 1985/86 and the two meet Jean Grey for the first time which is shown at the start of 'X-Men the Last Stand'. Xavier is shown to still be walking so it’s an easy assumption that he’s still on Hank’s serum at this point in his life.
Now, this doesn’t answer your question perfectly, theirs still other small continuity issues with the opening of ’The Last Stand’ which are: at the time of finding and meeting Jean Grey we can assume that Cerebro was used in discovering her and I imagine it was used to locate other mutants like Cyclops and Storm. Also, during the meeting of Xavier, Magneto and Jean, theirs a moment where Charles talks to Jean through Telepathy. So if Xavier is still on the serum, how was he using Cerebro since his powers were negated and how was he able to talk to Jean while he was walking. Theirs no official answer to this, not even a hint. So my theory is Xavier was still addicted to the serum but was willing to kick the drug for small periods at a time to reclaim his powers and use them to find new mutants. After he would find them he would resume the use of the serum and now that he was powerless he would have Magneto come with him as both a body guard but also as someone who could demonstrate to any sceptics that they were indeed mutants. You can still poke holes in this as it doesn’t explain the telepathy between him and Jean so the only thing I can surmise is that Jean was using her powers on him and he was acknowledging it like Magneto did too but the wait the scene unfolded it definitely seemed like Xavier was the one using his powers.