From their site:
"MooTools is a compact, modular, Object-Oriented javascript framework designed to make writing extensible and compatable code easier and faster. Mootools lets you get the job done efficiently and effectively."
While I have never heard of them, I would assume that based on the fact that they are a javascript framework, that, Yes, you probably can use them with ASP.NET. They are not mutually exclusive.
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Peter