What about people who fear snakes? Mice? Dogs? Clowns? The open ocean?
NSFW is specifically for separating out material that could get someone in trouble in a setting such as work, school, or public transit. It is also used as a NSFL filter for gore and other highly unpleasant things that users may want to self-censor (although the two really should be distinct, but most platforms don’t support that).
Unlike many other old Internet customs, NSFW has survived and continues on to this day because people recognize its importance and are generally good about using the tool appropriately. Marking posts that do not actually fall under standard definitions of “inappropriate” (e.g. nudity) only serves to dilute NSFW, to weaken it as an Internet self-censoring tool, and to weaken it means to increase the likelihood that it will be discarded.
NSFW is a critical element to keeping the Internet free and open, because it provides people with a way to control their experience and modify it as needed (for instance, allowing a user to easily avoid images when in a public space like a waiting room and not when in a more private environment). Once you start applying this tool willy-nilly, not only does that increase the likelihood of people ignoring the warning in a future (“I’m going to click this link because it’s probably just a spider or something… and it’s boobs”), but it also opens the door to pressure to use the NSFW label in malicious ways (such as to censor a gay couple kissing because “it bothers some people and doesn’t hurt to blur the image for them”).
Without tools such as the ability to effectively self-label material as NSFW, the inevitable conclusion is the banning of said material (“users aren’t using NSFW filters appropriately, so we just won’t allow that content at all, problem solved”).
tl;dr: overapplication of the NSFW filter is bad
This is the Internet. We are all exposed to things that we don’t like but that don’t bother other people.
I despise seeing photos of needles (especially in use), but especially ever since COVID, I’ve been frequently exposed to photos of needles, such as with articles about vaccination. When I see such an image, I squint and keep scrolling. Because this is my particular dislike, and therefore my responsibility to minimize personal exposure. But I would never suggest, nor even want, such images be censored. Putting NSFW on a vaccination image might make me more comfortable, but it would also further stigmatize what is actually a good thing at a time when it’s being attacked by anti-vax people and orgs. Similarly, spiders are good things (they fill important ecological roles, and are living creatures that deserve respect), yet many people squash them with disregard because they’re “icky” or “scary.” By censoring a completely normal photo of a spider on a general public forum, you are only serving to further the narrative that spiders are scary, unpleasant things that humans should actively separate themselves from.
If you’re still concerned, you can always put “warning: spider” in the title, or only post spider photos to bug-oriented communities and similar. But frankly I think you are unnecessarily babying a small, arbitrarily selected portion of the population. Again, do you similarly try to protect people with other phobias, or just arachnophobia?