No. Local hidden variables can not explain experimental results of QM without implying something many people find distasteful. But no one has demonstrated any objective reason why that distaste has anything to do with the universe or its laws.
So, another way to say it is local hidden variables do explain experimental results of QM if you are willing to accept the implications, none of which contradict observation.
There is this essentially religious notion of "free will" that physical theories have been obliged to preserve, for no objective reason. Hidden variables are inconsistent with experiment only if you demand "free will" be preserved.
You call an interpretation you don't like "nonsense". But calling a thing nonsense is not a way to refute it. Relativity was nonsense, once. Can you devise an experiment that may produce results inconsistent with the interpretation?
That's the same argument every model has made for the history of science, but :shrug:. The value of a model is its predictive capability. Thinking any one to be absolute truth blinds us from progress.
Local hidden variables can not explain experimental results of QM. That's a fact. Ask any QM Physicist and you'll get the same answer.