No, horseshoe theory is just liberalism trying to distance itself from fascism, when historically liberalism abd fascism correspond to capitalism doing okay and capitalism in crisis respectively.

Further, liberalism has also been responsible for mass violence, both the progressive kind such as in the French revolution, and the horribly reactionary kind when it comes to slavery, colonialism, genocide of Palestine, etc.

Your comment has one major flaw: it's wrong.

Revolution in France, for example, ovethrew an oppressive monarchy. Napoleon took power, but it was still an improvement, and in the long run was even better. In Haiti, slavery was overthrown, in Algeria colonialism was overthrown. These are just for national liberation movements and general revolution.

Socialist revolution in Russia, China, Cuba, Vietnam, Laos, Korea, and more have all dramatically improved key metrics like life expectancy, dramatically democratized society, increased literacy rates, and lowered disparity while dramatically developing society. Socialism achieves far better metrics at similar levels of wealth and development, even in the face of brutal sanctions.

There is no "betrayal of ideals," there's the real process of existing in the world and facing real struggles. Socialism isn't magic or perfect, it's simply a much better economic system than capitalism. It isn't immune to problems or struggles, and it doesn't gift those running the economy with prophetic visions. Liberal anti-communists hold socialism to a higher standard than liberal systems, refusing it outright if it isn't heaven on Earth, and call it a "betrayal" if it isn't immediately a perfect wonderland while giving liberalism a pass, or mild critique.

I expect revolution in the US Empire to go a similar way, only that it won't be at risk of being nuked or sanctioned to death by the US Empire.

I highly suggest doing more research on the topic at hand, I can make recommendations if you want.