Yes it is true. And no, AFAIK you don't need to go to Red Mountain. There are three (two?) groups of vampires scattered about, for example there's one group in a dwemer ruin. IIRC, you have to get bitten by a vampire (ie while attacking it), then if you don't cure it within a few days you become a vampire. I'm not exactly sure how you join the vampire clans - maybe when you go see them when you've become a vampire they don't attack you on sight.
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