If only EPP parties were really right-wing. I say this as an actual conservative. EPP parties generally are "our position is whatever the left espoused ten years ago". Which is, basically, a very progressive position.

Traditional European parties have been converging towards the center. That's largely thanks to the EU, which is a centrist project founded on ideas such as social liberalism and pro-market policies. Social democratic parties have also become pretty right-wing by their traditional standards, largely due to Third Way politics that have been dominant since the late 90s.