Evangelicals have lost their sway in life, absolutely. As has every other religion except for Islam. I am no supporter of Islam, by the way. But the reason the evangelicals have lost their sway is because they have extreme value and have erected mega churches and try to ram their ideals down peoples throats.
Studies are showing that the practice of religious traditions is declining and an increase in people identifying themselves as spiritual and not religious. People have so much access to information today that we are able to form one our opinions about important issues. Evangelicals are showing the hypocrisy of religion that steers people away.
I am personally not an Evangelical and I don't agree with a lot of things that they agree with, but they seem to believe the same things that they used to. To them, everything is the same and their positions on things is the same. I don't think the rest of the world sees it that way, but they do.
The Evangelical Christians were never all that massively popular to begin with. They were courted during Bush The Lesser's term in office, because they are a sizable enough minority to swing votes in states where needed. But I think that most people are sick of these so-called Christians and their messages of hate and damnation.
It used to be that evangelicals had a lot of clout in society. For example, the religious right often went against Disney, but sometimes what they thought they saw in animated movies turned out to be something else and completely innocent. Because of this, there was more ridicule about them than people believing what they said. It's possible for the religious right/evangelicals to gain more respect in society, but it needs to be done via being less reactive about things. I say this not as an outsider, but as an evangelical myself.