When Republicans did the heavy lifting to pass the civil rights law, were they playing the long game?

No.

You're confusing 20th Century Southern Democrats with today's liberal Democrats. 20th Century Southern Democrats were conservative Democrats from southern states that opposed the Civil Rights movement, after the 1964 Civil Rights Act was passed many Southern Democrats left the Democratic Party and joined the Republican Party. That's how Republicans got the Southern vote for generations.

It was after the passage of the Civil Rights Act and Southern Democrats switching parties that the parties became known is general as conservative Republicans and liberal Democrats.

Not as such. Party politics was simply very different back then.

These days, the Republicans are generally a reliably right-wing, conservative party, and the democrats are a left-wing liberal party, overall. This is actually a fairly new development. Go back a few decades, and both parties were actually fairly central overall, with strong liberal and conservative factions in both parties. Over time their positions have changed on different matters. For instance, the Republican party was originally founded as an anti-slavery party, later becoming one of the two dominant parties and now a more conservative party, and so forth.

Basically, even though the organizations have remained the same, their political views and stances have changed. Occasionally people refuse to acknowledge this- for instance, I still to this day see this argument advanced, mostly claiming that the Democratic party is a pro-slavery party because its original form over a century ago was one, but anyway. It's a weak argument to say the least.

To use another example, the modern day NRA is nothing like its original form. The NRA was actually formed to promote the teaching of firearms and shooting on a "scientific basis" and actually supported gun control laws- the head of the NRA in the 1930's testified to Congress that he believed guns should only be owned under-strictly regulated licensing. Over time its positions have changed to say the least, mostly since the 1970's.

Not really. Democrats were. They enslaved black people all over again. Through welfare. And they broke up their families ensuring they would "vote Democrat for the next 200 years".

Pathetic racists, those Democrats.

Liberals did the lifting. Many were Republicans at the time.

The republicans didn't do anything for the Civil Rights movement. It was the democrats who fought to pass Civil Rights. It was the republicans who fought to keep Jim Crow Laws in existence. The republicans are the ones who implement legislation on purpose that will keep black Americans oppressed and in poverty.