When did the conservative/liberal alignment take place?

[Orser67]

One could make a reasonable case for a few different years, beginning in 1896.

It's complicated by the fact that 20th century Democrats essentially had two "wings": a liberal presidential wing and a conservative congressional wing. This resulted from the fact that Northern Democrats tended to be more liberal than their Republican counterparts, but Southern Democrats were generally more conservative than either group (at least after they turned against the New Deal in the mid-1930s). These Southern Democrats often dominated Congress due to their ability to win uncontested elections in the one-party South, thereby gaining seniority and committee chairmanships, but Northern Democrats elected more presidential delegates and generally nominated one of their own for president (except in the last quarter of the 20th century).

In presidential elections, the Democrats nominated the more left-wing candidate in pretty much every election after 1896, with the major exception of 1904 (there also wasn't a huge amount of ideological difference in 1924, 1928, and 1976). However, conservative congressional Democrats remained quite important until at least the 1994 elections (or they may even still be important today, depending on how broad you define the term "conservative").

[Orser67]

I have yet to hear a coherent argument from anyone anywhere that there was a time when the Democratic Party was clearly more conservative than the Republican Party, on average.  Period.  The arguments ALWAYS lie on lazily founded shortcuts like "the GOP used to win the Black vote, and look at how Southern Whites and Blacks flipped" ... okay, you're telling me NOTHING could have contributed to that besides two parties completely flipping ideologies (I really don't think people stop enough to appreciate how RIDICULOUS of an idea that is)?  Or "the Democrats used to support states' rights, and now the GOP does!"  So?  Lol, seriously, that is not an argument whatsoever.  Or, "the GOP employed the Southern Strategy to win racist Whites!"  Uh, yeah, DUH ... so what?  A conservative party tried to get more voters, and they were voters that used to vote for the other party ... that does not, in and of itself, imply that 1) the GOP wasn't just as conservative before incorporating these new voters or 2) that these new voters weren't less conservative than before joining the GOP; we have all seen how well voters chameleon themselves to fit their new tribe.  RE: any 1960s arguments, Mad Men ironically does a very good job of showing how a switch in voters does NOT mean a switch in ideology.

I'm wary of conflating 19th century liberalism with 20th century liberalism, but it's certainly true that historians generally consider Jefferson and Jackson to be on the left of their rivals in the Federalist and Whig parties.

However, in the late 19th century, I would argue that both parties were fairly right wing. After the Democrats rejected "soft money" in the 1860s, there was very little difference between the two parties on policy other than the tariff and support for the protection of African American civil rights (which was still favored by many in the Republican Party until the late 1890s). The parties essentially became ethnocultural alliances competing for government patronage. The conservativism of the two major parties helped give rise to the Populist Party, which called for an inflationary monetary policy, progressive taxation, federal regulation of railroad rates, and various other interventionist measures designed to help the working class. The Democratic Party's nomination of Bryan for president signaled an endorsement of populist policies, as well as a total repudiation of Cleveland's conservative policies.