Is Singer going to ignore X-Men: The Last Stand?
Vaughn described it as a "loose prequel". I don't think Singer and/or Vaughn are going to be beholden to the continuity of the series in any significant capacity. I know Singer talked about choosing characters that would make sense to feature in
First Class (Beast because he appeared much older in
The Last Stand; Mystique because her age was never really mentioned, and in the comics, apparently she ages much slower as part of her mutation; etc etc).
However, as
Captaindemotion pointed out, several elements of
X-Men: First Class directly contradict what happens in
X-Men: The Last Stand and
X-Men Origins: Wolverine, and even to be technical, one aspect of
X2 (Dr. Hank McCoy appears, pre-transformation, in a cameo appearance; however you could easily pull a comic-book explanation and say he was using a de-visualizer as he's done in the comics).
I would say
X-Men: First Class has a "vague history" when it comes to following the continuity of the first four films.

I think it was Vaughn who mentioned that if they did sequels they would gradually move more and more away from strictly adhering to continuity and become more of a reboot/fresh start. He kept on mentioning
Casino Royale as a particular example, however he could have been just mentioning how that series took James Bond back to his roots, and by extension,
X-Men: First Class appears to be doing the same with the X-Men.