Sure, this is no fun, but this whole discussion exists because trolls exist: can we really expect anything pleasant to come out of that premise.
Someone is not a "bad-faith" actor for asking precisely the questions that are hard to answer, even if they're using those questions to support a wrong idea.
If you don't have time to answer their questions, don't answer them. If you do have time, you have a good opportunity to expose the falsehood of their ideology. But don't use ad-hominems like "sealioning".
Sure, there are some stupid questions, or questions that come with a false premise, but that's not the same as discounting good questions because they come from an anti-vaxxer.
Yes, just saying someone is "sealioning" is lazy at best, trollish on its own at worse (as I have already said in the previous post). Saying "your argument is fallacious *because* of A, B, and C", is pretty much the only way to deal with a troll (besides just banning them from the platform). In the particular example of sealioning: certainly, never assume bad-faith, but after you briefly explain and give references, it is definitely very important to also explain to the person how sealioning is a dangerous tactic - at best, you helped someone be more resilient to sealioning themselves, at worst you lost some time with a troll.
The one thing I would agree on with you: if you come in on a high horse, you have already lost the discussion, no matter whether you are talking with a troll or not.
1. Labeling someone a "sealion" doesn't even hinge on their opinion. You seem to have missed the entire concept, and instead interpreted it as a generic dismissive.
2. Uh, you don't get to just call something a "fallacy" because you don't like it (though many others are doing the same thing in this thread).
Sealioning is a reference to the specific disingenuous process of spamming the same low-effort, low-brow, easily-answered questions in every last public forum. It's a basic disinformation technique to spread fear, uncertainty and doubt.
If you look at the original comic[1], the sea lion follows the couple around in public, into their house, and even into their bedroom, without permission; that is what makes the sea lion's behavior bad (criminal, in fact). However, "sealioning" in practice refers to people responding to public internet comments with other public internet comments. To treat the latter like the former is dishonest.
Furthermore, the sea lion is objecting to unsubstantiated criticism of his species, which is a form of bigotry. Imagine people searching Twitter for criticism of, say, their race or religion and arguing back at it. I suspect that 90+% of those who complain about "sealioning" would consider that behavior permissible and probably downright virtuous (and would add that the arguing-back need not be scrupulously polite). I'm frankly surprised that "social justice"-associated people managed to decide that objecting to speciesism was worthy of mockery. I think they just really wanted some term of disparagement for their opponents, and happily accepted this one when it appeared without analyzing it too closely.
The internet is a fun place.
Edit: Well, as the comment below alluded to, I probably missed a pretty obvious piece of sarcasm... This is certainly funny in hindsight.
Basically, it is now impossible to make a point by attempting to present an absurdly extreme viewpoint in the opposite direction, because too many of us have encountered people who genuinely espouse viewpoints even more extreme. (As well as the exact one you said—no matter what it happens to be.)
If you want to present such a thing sarcastically, you're gonna have to make an explicit indication of your sarcasm (even just a "/s" at the end is usually enough). Otherwise, you're very likely to just be taken as meaning it sincerely.
But of course we all know confronting someone directly about their opinion always works.
I'm entirely pro-vaccines. However, I'm simultaneously entirely in favor of people asking questions, no matter what their intentions are. Their intentions do not matter. You either know your stuff or you do not. It's always better to draw out the eg anti-vaccine types. If something is defensible, then don't be a coward about it, don't be lazy, respond with a decent answer. Put in some effort. Use it as an exercise for your own brain, your own beliefs, your own ability to discuss and debate in an (ideally) civil society. Only the anti-vaccine arguments benefit from not doing that.
The shut-down angle always comes from cowardice and or intellectual weakness. You can tell a lot about someone by whether they're terrified of a discussion. Shut-down attempts are meant to evade personal shame (and more rarely to avoid putting in the time/effort), while preserving an intellectual or moral foundation established by someone else who did put in the effort.
Nearly all shut-down attempts come from weakness. If the position is important, such as vaccines, then that weakness only encourages the skeptics even more. They can practically sense it. The right thing to do is to engage and push back with facts (and or even links, with which all the hidden passive readers can go make up their own minds as to whether they agree or not), even if you don't have all day to argue a topic.
For some of them, their entire method of operation is to waste your time, troll, and gain acclaim from their own hardcore fan base by doing so.
I'm sorry to say that I have no time and effort left on my part for anything other than low effort mockery and derision of people engaging in infowars/hardcore conspiracy theory stuff.
This is why good journalists do not invite a "flat earther" and a "nasa scientists" when discussing, e.g., climate change. Because those organizing debates have a responsibility to ensure the debate is based on facts, not on oratory skills.