... implying they don't already have an "easy button" in the form of the Winter Soldier plot. "Hydra infected the highest levels of government and had a machine crawling all variables about all people via social media data gathering. They discovered mutants and buried the info to be used later. When Rogers foiled their plans the information was lost, as it wasnt what he was immediately looking for (distracted in his quest for Bucky)."
Heck it writes itself as a Hydra fueled holocaust if you really wan to "modernize" it. Mutants were round up and enslaved/experimented on. It was done in some abandoned holocaust camps which made the perfect cover as they were already built for the purpose. OMG Wanda was mutant the whole time! The twins were experimented on with the cube _because_ they were experimenting on Mutants!
There, in 30seconds I gave two paths both which "fix" the time problems as well as any movie ever does and gives you the option to leave Magneto as a Nazi OR Hydra survivor. Take your pick.