Leftism isn't some holy vow, it's a practical working mindset to work towards Socialism. There can be no real progress for humanity while the United States remains the worlds largest empire, the US is the biggest barrier for Socialism worldwide.

Ultimately, when you simplify everything down to only supporting genuine Leftist movements, you find yourself without even temporary allies who may have otherwise shared a common goal, and this lowers the chance of Socialism succeeding in the long term. In other words, you would refuse to support the Union over the Confederacy, or Palestine over Israel. This is a convenient oversimplified worldview to take, but it isn't siding with the global Working Class, but just Leftists specifically.

In other other words, if you refuse to even make temporary allies, you aren't taking "anti-billionaire" seriously.

The situation is more complicated than your comparison and your analysis shows a fundamental lack of understanding about what critical support is or why it's given. It only appears like cherry-picking when you don't understand the underlying reasoning that informs these decisions and how they are consistent with Marxist-Leninist theory.

A better metaphor for comparison is if you think of Putin as chemotherapy. Chemotherapy is poisonous, it's bad for your body, and enough of it will kill you. It sucks and it hurts to go through, however, it also kills cancer cells (weakens US/Western hegemony/imperialism). No one likes chemotherapy and everyone recognizes that is bad for your body, but we suggest the use (critically support the use) of chemotherapy in the fight against cancer (Western Imperialism/capitalism) because it helps us progress toward our ultimate goal.

If the West had allowed Putin to join their hegemony as he had always wanted, then there would be no critical support for him from MLs because all the geopolitical waves he makes that are destructive towards the Western imperialist geopolitical waves would not exist. Anytime you see an ML saying "I love you daddy Putin" please understand that it's a joke. People misrepresent our positions all the time and we cope by embracing them in jest. He's a capitalist pig who we'd like to see gone or reformed like the others, but he's a strategically useful pig in that his actions are weakening Western Imperial power in the current moment. By the ML definition, imperialism = capitalism (it's just the stage we are in) and the biggest base of imperial power comes from the US. Once the bigger threat is defeated, if he's still around and up to capitalist bullshit, Putin will not have our support. While his actions help support our goals, it makes no sense for us to actively oppose him when we could better spend that energy elsewhere. It's similar to "the enemy of my enemy is my [strategic] friend". ML prefers an approach that is more focused on pragmatism than ideological purity.

Not all leftists agree on this type of critical support. Typically, those are the ones shouting for more purity and are typically who we call ultras. The same reasons they would not critically support Putin are the same reasons they don't support China and call it capitalist (a focus on ideological purity rather than a practical approach toward achieving our goal of communism).

If you want to better understand why certain leftists do what they do, there is plenty of material out there explaining leftist theory and contemporary geopolitical analysis. Likewise, you could always ask us why we take certain positions on Lemmygrad or Hexbear. There is likely someone happy to take the time to explain or a well written explanation that already exists that can be linked for you if you show genuine interest and a willingness to listen, though you should be warned to expect some prickly responses in those spaces due to people who asked before you and turned out to be trolls.

The extent of the energy I'm willing to spend on the topic now ends here. Hopefully it helped clarify what we mean by critical support.