They agree on few things and disagree on most. Horse shoe effect is just a way how to dismiss actual real politics and ideologies so one can wave hands.

They disagree on a lot of things, but they also disagree on a lot of things with moderate people, so that observation alone doesn't refute "far-left and far-right are closer to each other than they are to the center".

Of course the horseshoe effect is not some objective truth that's true in every country, that would be silly. I think the interesting part of it is that extreme ends of any political spectrum experience a similar environment: they are often shunned, distrust the mainstream media, attract social outcasts, etc. Just the shared experience of being on the edge of the spectrum often leads to similarities between them.

But (as stated) they disagree on most things. Because they are both usually in the opposition to the governing parties, they do opposition work and present dissenting opinions on vaccine efficacy, war support etc.

Often these few common topics overlap with the libertarian viewpoint.

I don't understand that argument. If the government supports a war, doesn't that make any opposition parties more likely to agree with each other that the war is bad? Of course they can disagree with the war for different reason, but both parties being in opposition and dissenting still makes them more likely to have common ground.

Edit: unless we are talking about one or two party systems, there the dynamics are stranger