Whether or not you decide to keep them is up to you - some people like them, others think they’re not worth the risk. To help you decide if they might be worth the risk, here’s a sizable info dump.
If you keep them fed and have your tank set up to hold them (i.e. make sure they can’t get sucked into powerheads/filters, make sure they can’t torch themselves on your heater, etc.), then they are typically beneficial.
However, from what I’ve read, it seems literally all sea cucumber (medusa worms included) do have the toxins you’re concerned about to some degree or another. The part that’s hard is that how much toxin the cuke contains and how likely a cuke is to release those toxins varies from species to species. Some species are substantially more prone to releasing the toxins than others, and some release a good deal more of the toxin than others. An important note here, the toxin of sea cucumbers (holothurin) is an ichthyotoxin (it primarily affects fish, though in high enough quantities it can affect other things like inverts and people too), so if the cucumber does release its toxin into the tank, the inverts might be fine. For more info, here’s a post I made referencing and expounding upon another of my posts on the subject from a while ago:
As mentioned, many sea cucumbers will release toxins when stressed/dying, so it's important to keep them happy and to be prepared to deal with that situation should it arise (i.e. be prepared to do an emergency water change, add carbon, transfer livestock to a hospital tank, etc.) - some cukes are highly toxic, some only mildly, some release toxin when stressed, others only release it once their corpse starts to decay, etc. so the risk varies a lot depending on the species, but unless they're one of the highly toxic species (like Sea Apples) it's not usually too big of a concern. Plus, many species will give warnings that they're dying/stressed, so sometimes people are able to get a heads up that they need to remove them (see my quote below for more info).
ISpeakForTheSeas said:
Some sea cucumbers like to just pick a spot and stay there, so it might just decide not to move. Given that you said this one started real small and kept growing, it's possible you just had all three come in at the same time, possibly from the same batch of baby sea cucumbers. If that's the case you either could have just missed them because they were so small, or the other two may have just moved over there because the conditions there are more favorable for their larger size than the previous area they were in.
Regardless, most sea cucumbers are generally safe in reef tanks (not much tries to eat them, so generally you don't need to worry about them getting overly stressed), but you should probably make sure your equipment is sea cucumber safe (i.e. you want to make sure they can't get pureed by going into one of your powerheads or something), and - as was mentioned above - they can release toxins when they die, so you'll want to keep an eye out for that. A lot of sea cucumbers will give you some sort of warning before they die (such as contracting to look short and squat - a defense mechanism/sign of extreme distress that they use to try and escape predators/death - or ejecting a cloud of toxins - because of how this actually works, the cucumber generally dies after releasing the toxins), and some of them, as long as they don't get hyper distressed, (as I understand it) won't intentionally release toxins in your tank - they just die like a normal animal, so as long as you remove the body fast enough, it won't poison your tank.
On the off chance that they do decide to release toxins into your tank, if you catch it early enough, you can run carbon, do a big water change, and (if necessary) transfer your livestock to another tank. I would strongly recommend using protective equipment in this case as some sea cucumbers when they release toxins can be dangerous to humans, but, ideally you wouldn't need to worry about it. Ideally, you'd just remove the cucumber either soon before or soon after it dies (the people I've talked to said they didn't need to run carbon or anything when theirs died in their tank, so as long as you catch it before the body starts degrading you should pretty much be fine as I understand it).
Lots of scary info there, but generally sea cucumbers are safe to keep, and as long as they are physically safe from harm in your tank the chances of them "cuke nuking" it by releasing toxins into your tank are very slim.
Hope this helps!
TLDR; nem guards are good idea for sea cucumbers.
