Will filtering salt water through a coffee filter make my cats drinking water safer to consume?

My cat Wallace is my most precious thing in the world. I live near the ocean which means I always have a source of fresh water, this "off the grid" lifestyle I chose means even my animals need to have the same diet as me. I noticed my cat has been vomiting regularly and meows at the window whenever it... show more My cat Wallace is my most precious thing in the world. I live near the ocean which means I always have a source of fresh water, this "off the grid" lifestyle I chose means even my animals need to have the same diet as me.

I noticed my cat has been vomiting regularly and meows at the window whenever it rains. I think the salt water may have something to do with it, but i've been filtering it through a coffee filter every time so it just doesn't make sense.
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