Another question about your tax money paying for healthcare

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I've read a wide variety of opinions here about who should and should not receive government-funded healthcare. Some people say they don't want their tax dollars being used to pay for healthcare for anyone, some say they're okay with funding for everyone except undocumented immigrants, and others say any variation on the spectrum in between. (I'm not including those who say to pay for absolutely everyone, because my question is not for you.)

Here's my question for those of you who would exclude any person or group: If we had an outbreak of TB or the plague or some such disease, would you change your mind?