Are we really wired for it, though? I've personally never had that fear.
Perhaps it's a little more nurture than nature?
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In Experiment 2, observers watched edited videotapes that showed models reacting either fearfully to toy snakes and nonfearfully to artificial flowers (SN+/FL-) or vice versa (FL+/SN-). SN+/FL- observers acquired a fear of snakes but not of flowers; FL+/SN- observers did not acquire a fear of either stimulus.
In Experiment 3, monkeys solved complex appetitive discriminative (PAN) problems at comparable rates regardless of whether the discriminative stimuli were the videotaped snake or the flower stimuli used in Experiment 2. Thus, monkeys appear to selectively associate snakes with fear."
Experiment 1 shows that monkeys become afraid of snakes through watching videos of other monkeys being afraid of snakes. Experiment 2 shows that monkeys don't acquire a fear of flowers if shown a video of other monkeys being afraid of flowers. Experiment 3 shows that monkeys can still be conditioned in other tasks using videos of either flowers or snakes.
Further, if there's a learned fear of snakes, that might not be coincidence, even if it's not genetic.
"Although considerable controversy has existed over the extent to which this fear of snakes is “innate” as opposed to based on learning, current evidence suggests that learning is necessary for the fear to manifest itself, at least for some primate species in which wild-reared but not laboratory-reared monkeys show a fear of snakes (see Mineka & Cook, 1988, for a review). For example, Mineka and Cook demonstrated that laboratory-reared rhesus monkeys who were initially unafraid of snakes rapidly acquired a fear of snakes after watching wild-reared model monkeys exhibit a strong fear of snakes (Cook, Mineka, Wolkenstein, & Laitsch, 1985; Mineka, Davidson, Cook, & Keir, 1984). The naive laboratory reared observers initially reached rapidly for food placed adjacent to a series of stimuli, including a real snake, toy snakes, and neutral objects."
Humans are wired for noticing snakes. There are neurological mechanisms [1] that have evolved in humans to prioritize visual detection of snakes [2] and other common threat-related stimuli. I don't know what the science says about this perceptual mechanism being inherently linked to a fear response, but it would make sense given the hypothesized selection pressure that gave rise to it (i.e., not only noticing, but avoiding, the snake before it bites me raises the chances my genes will be passed on)
1 - https://en.wikipedia.org/wiki/Feature_detection_(nervous_sys... 2 - http://childstudycenter.rutgers.edu/Publications_files/LoBue...
An analogy might be, many people are afraid of heights, and fewer people are afraid of water. That's despite the fact that water is also dangerous. But none of this proves or disproves the notion that fear of heights may be "hardcoded".
If you had a lifelike stuffed tiger and you posed it in contexts where it wasn't immediately obvious that it wasn't real, I bet you'd get some amazing startle reactions. It sure works with dinosaurs, even though dinosaurs haven't existed for millions of years: https://www.youtube.com/watch?v=DSup2gj2Gn4