Random vampires cannot turn your Sim into a vampire. At worst they break in, drink from your Sim and disrupt their sleep. I rarely have this happen and it seems to be easily diminished by NOT introducing your sim to any vampires, and for me the more annoying part is when a vampire "breaks in" to a community lot because they stay and drink at the bar or something while the game refuses to let you go home until they leave.
The main question to ask yourself is this: do you want your Sims to have a little more personality and diversity? That is the selling point that makes vampires potentially worth it even if you don't like supernatural aspects. The ability to choose powers and weaknesses makes the Sims far more customizable than the actual personality traits. This game suffers from very weaksauce personality traits that often aren't even noticeable, but because the vampire powers are things like not needing to shower, being able to instantly seduce anyone of the opposite gender, very powerful moodlets for things like Sun Phobia or drinking from a Sim without permission if you have a morally good Sim that hates doing so (the moodlets tend to be a minimum of +3 and as high as +10, thus overriding happy moodlet spam with ease), this means the vampires actually tend to have more personality than all of the base game traits combined.
I would take a look at the powers and ask yourself if it sounds like things that you could make diverse Sims with that you enjoy playing. If so, you may find you're now willing to get over any dislike of supernatural aspects simply because the quality of the game and sim diversity spikes. If you're still unsure, then understand that WORST case scenario, the vampires break into home, drink from your sim to disturb their sleep, and sometimes prevent you from leaving a community lot. (though this is a bug that they should honestly fix) You can even diminish the frequency of those by simply never introducing yourself to vamps or associating with them, as well as moving out and deleting the two preset families.
I'll also just add I used to hate Supernaturals too. I wanted realism. Since Sims 3's pack though, I've changed my tone because quite frankly I think supernaturals and other lifestates over tremendous potential for gameplay and variety, so I'm more than willing to compromise some realism for that.