I'll start by noting that this question wasn't closed by moderators, but by members of the community. The community can also re-open it. Below is why I, personally, am not voting to re-open it - but I would respect the community choice to do so.
Several commenters argue that the question should be asked on Politics.SE. I agree that it seems a good fit there, but that doesn't mean it isn't also a good fit here. That's not a Close reason, but it is a good suggestion to the OP about where to go next.
However, @ThunderForge linked to an existing Politics.SE question: Why have the Democratic Party and Republican Party switched positions on civil rights since the Civil War?, and the answer was very illuminating. It made a good case that the ideologies hadn't switched, if you just looked at them from a different level.
I am not saying that this answerer [Oh! Look! It was our very own @Brythan!] was right in their argument, but it demonstrates that the claim of ideology-swaps is a matter of perspective and opinion, rather than simply what the evidence reveals. Those sorts of questions aren't great fits for Skeptics.SE. That is the main reason I agree that this question should remain closed here.
Minor issue: The unreferenced meme doesn't make the claim that the ideologies of the parties has swapped. In fact, it relies on the opposite to make its implied point that the Democrats are against progressive ideas. A reference to someone actually making the "common explanation" would improve the question.
Referring "at some point" in the question and "the event" in this meta-question, implies that the alleged switch was a relatively sudden point in time, rather than a gradual evolution of their views.
Suggesting that modern Republicans might have the exact same ideology as pre-civil rights movement Democrats is rather unfair. I do not believe that such a small number of today's Republicans would vote to repeal slavery, for example. The ideologies haven't been an exact swap, making the question just that little bit more vague - a more precise claim would help.