Good grief ...
"There is a very high-level principle that says that something and its opposite can not exist at the same time." Nonsense.
The principle you might mean to invoke is better stated as "A thing may not both be and NOT be at the same time." You illustrate this in your next sentenced quite clearly.
"Any science that claims that a "cat" can be alive and dead at the same time is invalid." Again, nonsense.
NO 'science' claims this. Schroedinger used this imagery to illustrate a 'thought experiment' concerning the emerging model of Quantum Physics. ( N.B. No actual cats were harmed during the production and discussion of this model. )
To proceed from these defective premises to the conclusion that 'particle physics is not a true science' is simple evidence of deficient reasoning.
Or was that all cats were harmed. I can never keep it straight..