I'm going to disagree with the folks saying to just ignore the anti-vaxxers.

These people are not cranks, in the sense of the proposed duplicate question. A crank in that sense is an intellectually isolated person who is merely wrapped up in their own personal eccentricity.

The groups opposing COVID-19 vaccines include well-funded and purposeful organizations that have in many cases become linked with politics. You may not be able to stop them from citing your work, but you can certainly make a public statement explaining that they should not cite your work and why they are wrong to do so. There's no point in having a public fight with a harmless trisector, but there's a damned good reason to have a fight with a group that is actually effectively working to undermine public health.

The question is: are you up for the potential of a public confrontation? They'll probably just ignore you... but they might not. They might add you to their cast of villains, and that might or might not be a risk that you feel able to afford.

Bottom line: I believe that ethics indicates that you should oppose the use of your work in this case. The only question is how much you feel is an appropriate investment of energy and taking on of risk given your current personal and professional circumstances.

Dan Pfeiffer* has a great article about combatting misinformation without bringing it more attention. I believe it's largely relevant here. The most relevant section† is here:

The gist of this argument is that the only way to [combat misinformation] is to shine a light on it. Sunlight is the best disinfectant. The point is not wrong. We cannot ignore these dangerous trends [...] But how we shine that light matters:

Quote tweet your friends, screenshot [misinformation]: This is an online engagement rule from Dash: If you need/want to push back on disinformation or highlight a dishonest or dangerous statement, using a photo of the statement allows you to make your point without giving the troll the information they need.

Don’t spread disinformation: If you respond to disinformation for the purposes of debunking it, you are inadvertently instructing the algorithm to show the offending disinformation to more people. You can either use the screenshot trick above or separately share a fact check or article that debunks the conspiracy theory.

In the context of stopping the spread of your paper being used for COVID misinformation, I would interpret the above guidelines to mean: Don't retweet or share the tweets containing misinformation, or link to other sites mis-citing your work, even to point out how they're wrong. Instead, create a tweet or a response on another medium from scratch, which can be shared and that fact checks in a way that highlights the facts − not the myths. The key is not giving engagement to falsehoods, and instead try to drive engagement to facts.

_{*former Senior Advisor to U.S. President Barack Obama for Strategy and Communications
†American political emphasis removed to specifically highlight how this technique is applicable to the question at hand}

I was in a similar situation: during a few radio programs with a homeopath and a magnetizer (or whatever the man who has cosmic power in his hands is called), I made informed fun of their "science". They were there to answer and it went sideways.

One thing I learned: their groupies are terrifying.

I was in my PhD phase at that time, and in a very hormone-powered confrontational mood so I went in headfirst.

It was great at that time, but I would not do it now (30 years later), for several reasons:

• I do not have the time I had
• I have a family and these people are nuts. They would literally make standups in front of your house. I was living on a campus at that time, so it ended up well (without going into gory details: not that well for them)
• specifically homeopathy companies have lawyers: when you tell them that their science is idiotic (because dilution, atoms and everything), they will drag you to court (I have to find a reference for that I read some time ago).
• After 30 years, instead of gaining the wisdom I was supposed to, I believe that these people should be made to shut the fuck up because they are a danger to society. So the discussion quickly turns to words usually considered unfit for a scientific discussion.

You really need to consider if you want to fight, and if you do, whether this is going to be interesting, amusing, fun, and energizing for you.

As a special note for my favourite subject of "the science of homeopathy" (closely followed by "religion and science"), I was trying with the homeopaths to settle the fact that homeopathy may very well work due to the placebo effect. When I take an aspirin, it does not even have the time to drop into my stomach and I feel that my headache gets better, see?

They insisted that there was a physical reason for homeopathy (memory of water, usually) and then we were done.

I also feel that people should understand that they pay 30€ for a placebo effect - which may or may not be fine for them.

Finally, there is the despicable class of preachers of alternative solutions such as these who will use the fear and despair of people and drag them from actual treatments to their crap, endangering their life.

As they say in Kingsman, needed to let off a little steam :)