It's very much a prequel to Singer's movies
Except for where it doesn't fit, such as the thing about Magneto helping Xavier build Cerebro.
Of course it's not going to have perfect continuity with Singer's movies. It's called creative license. They were trying to make the best film they could possibly make, and they didn't want to be a complete stickler to continuity. I get that.
Besides that, Magneto could still help Xavier build Cerebro. Hank might have designed Cerebro for the CIA, but at the end of
First Class, Xavier hasn't even opened up the school yet. In the comics, Xavier and Magneto's relationship was always rocky. They would go from being friends to enemies and then back again. At one point, Magneto was actually leading the X-Men, which I think would be an interesting topic to explore in a sequel.
So, ostensibly, Magneto could still help Xavier build Cerebro underneath Xavier's mansion. It's still feasible.