Fascinating. The majority in both parties want their party to move away from the left.

Not in the graphics but significant in these stats: 50% of Democrats identifying as liberal (a big increase in the last decade) , 70% of Republicans identifying as conservative (a fairly stable percent for the last decade and more) .
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Democrats Favor More Moderate Party; GOP, More Conservative

Given a choice, rank-and-file Democrats would prefer that their party shift to the center rather than the left, while Republicans favor a more conservative than moderate GOP.

https://news.gallup.com/poll/245462/democrats-favor-moderate-party-gop-conservative.aspx