Let's have some more current information, shall we?
https://news.gallup.com/poll/225074/conservative-lead-ideology-down-single-digits.aspx
"Almost all of the shift since 2001 toward the liberal label is the result of Democrats increasingly adopting the term."
Those "moderates" that don't identify with liberal or conservative? Yeah, they're slightly more liberal than they are conservative. It's not that they are becoming more liberal, per se - it's that they're becoming more comfortable with the term (or, more likely, uncomfortable with any proximity to the term "conservative" because of how readily conservatives have embraced Trump).
It's not about who has more hard-liners. It's about who has more of the middle. We do, and increasingly so.