Not only is "The only good Tory is a dead Tory" not a popular refrain at all [1], but a quick search for "The only good Republican is a dead Republican" returns a lot of hits for the "[...] dead Democrat" quote and almost none for the search phrase.
These attempts at false equivalence reliably appear in these situations, and there's reliably nothing to back them up.
The difference is the right is trying very hard to move the Overton Window and make "[...] dead Democrat" an acceptable mainstream sentiment suitable for national news.
[1] You certainly won't hear it from any left-leaning MPs or in Labour constituency meetings. And if that weren't true, recordings would be all over the media.