Sure, but that's taking the concept of what's "logical" to absurd extremes. Any sort of paranoid delusion is logical if you accept all of its premises.
Is being antivax logical? Not at all. It requires amazing mental gymnastics to ignore centuries of scientific research. Things that are "logical if you believe them" is a great way to describe things that aren't logical. Vaccines do not, in fact, by all available measures, cause more dangerous issues than the diseases they prevent. If your "logic" requires a rejection of the entire epistemological framework upon which shared scientific kknowledge is established it's not "logic", kind of by definition.
This is the same thing. Its internal consistency isn't "logic". It can be shown to not be logical. If you suspend yourself from that conversation, deny the parameters of anybody who disagrees with you and cherry pick your values to specifically support your instinctively desired conclusion, then it doesn't matter how well you can through your train of thought, it's still indefensible.
I think that's why the MAGA thing stumps you a bit. Their train of thought isn't any better or worse than this. It's, in fact, identical. Information that supports it gets magnified, information that disrupts it is ignored. They are fun about it in that they add this cool temporal dimension, where that selection is applied regardless of how it was applied before, so they're all for free speech when people tell them to shut up, all for limiting speech when people criticise them. But that's not different to the fundamental contradiction of being concerned about a population crisis when you are trying to turn women into walking incubators but concerned about the massive influx of people when you're trying to be racist.
It's a lot of things, but it's not logic.