Back in my younger days, 1950's, 60's, 70's, we never heard of the blue dog Democrats. Now most folks were yeller dog Democrats derived from the notion that they'd vote for an old yeller dog before they'd vote for a Republican. Blue Dog Democrats is something I never heard of until 2010 when the media tossed that phrase out to denote most of the 63 House Democrats who lost.
I'd like to present a chart from Pew Research on party affiliation to show the Democrats didn't really lose anyone in the 60's and 70's to the GOP, conservative or otherwise.
You can see those who identified or affiliated with the Democratic Party average roughly 45% of the electorate from 1942-1984. With its normal ups and downs. The Republicans chugged along averaging roughly 25% during that time period. 1984 seems to be the turning point when the Democrats dropped to an average of 35% thru 2008. 1984 just happen to be the year of the Reagan landslide where he won 49 states and beat Mondale 59-40% in the popular vote. The nation as a whole had a huge realignment political wise during Reagan which in my opinion carried through to and until Obama as even Bill Clinton governed fairly conservative.
https://www.people-press.org/interactives/party-id-trend/The big move these days is to independents, static from 2000-06 at 30%, independents have risen from 30% in 06 up to 40% today. Both parties have lost folks to the independent ranks. As of 4 Jun 2020 Gallup puts party affiliation at 31% Democrat, 25% Republican, 40% Independent. So the GOP is back to where they were pre-Reagan while the Democrats have dropped 15 points from the pre-Reagan era. Independents are the big winners.
Over the years there has been three huge realignments in voting habits, 1 the Northeast from Republican to Democrat, 2 the west coast from Republican to Democrats and 3 the south from Democrat to Republican. I should add a fourth, some state surrounding the Great Lakes, Michigan, Illinois, Wisconsin and Minnesota from Republican to Democrat. The Plain and Mountain states have remained Republican for the most part.
I think the numbers prove that the old yeller dog, conservative democrats of the 1960's and 70's remained Democrats for the rest of their lives. It was their off spring that changed and became Republicans. It wasn't until 1984 that the south went entirely Republican, but then again with the exception of Minnesota, the entire country, 49 states went Republican. Bill Clinton carried most of the south in 1992 with the exception of Alabama, Mississippi, North and South Carolina. So the shift has been more recent than in the 1960's and 70's.