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.
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 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.
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.