This reaction is almost certainly a taught cultural behaviour.
In some areas of the world, snakes/spiders are considered food sources. Many of these areas, such as the amazon, also contain the highest concentrations of venomous species.
There was a video that presented images very quickly and asked you to count spiders and snakes percentages among innocent pics. Most respondents (me included) evaluated to at least 50%, while real ratio was something like 1/5 or less. Also, when you watch it, it feels like snake-spider-snake-grass-spider-snake. You may not run in panic, but you do see it.
Cannot find the video, and it was probably a gif, afair.
On the other hand, chimpanzees raised in captivity have been known to scream in fear when seeing snake-like objects such as pieces of hose.
As far as I can tell, not being afraid of them has to be learned. I cannot find a source, but I recall reading that even people who keep spiders as pets, still have a raised heartrate when holding them.
There is a major environmental/learned aspect to this, I don't buy the 100% inborn argument at all. Young children (0-12mo) don't give a damn about anything. I do believe we are born with the innate potential to focus on these creatures faster/earlier than other animals, but fear, that's learned.