Going to mass weekly and receiving all the sacraments without giving a dime to the Catholic Church is a perfectly valid thing for Catholics to do.
If a Catholic does not want to give collection for fear of their money being misused, here are their options:
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If one wants to contribute money to the Church but are afraid that the money is going to be misused, one can give only to the second collections, and only on those whose goals your share and can verify that your money are going to the places that you want them. One can also donate directly to different organizations and institutions within the Church that does not answer directly to the Vatican.
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If one does not want to tangle with the Vatican at all, there are 23 Catholic Churches that are not Roman Catholic Churches. They do not answer to Rome but still possess the fullness of truth and the sacraments.
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One can, as you say, just not give any money. That’s perfectly fine.
Nevertheless, if you abide by the Catholic beliefs (your axioms), then leaving the Church because of the sex scandals is an incoherent position.