That is your opinion stated as if it were a fact.

Here are facts:

Anti-vax is a shortening of the term anti-vaccination, and it is not a surprise to find that people who are 'anti-vax' are against vaccinations, and many of them actively try to recruit people to their cause of avoiding vaccines. Anti-vaccination is a highly accurate term.

I and many others who are pro-vax don't think that anti-vax people are against a vast range of science-based medicines. To the contrary, I am amazed at how many anti-vax people will smoke cigarettes (DNA poisons) and drink alcohol (DNA poison) and take antibiotics and blood pressure medicines and see a dentist and see a regular doctor. Not to mention that many who are against a covid vaccine have had many other vaccines. This selective position against vaccines and not other treatments only makes their anti-vax attitude appear even more irrational.

But if you want different word, then vaccine hysteria would be a good choice. Because that's what anti-vax attitudes have caused, and now a few hundred thousand people have died from it. Think of the damage all those avoidable deaths will cause for millions of people.

I haven't seen a single comment in this thread that alluded to "I am against any/all vaccinations", which is why "anti-vax" is a bad faith term.

What is a neutral term?

I have been dealing with them in person in a clinical setting for a while now and struggle to see a non-negative side to the behaviour directed at myself and colleagues.

Anti-vaxxer here. While their negative behavior directed you/your colleges is reprehensible, I can tell you how I feel towards (most) 'vaxxers'. It's almost exactly the way me, an atheist feel toward religious believers. For course atheists come in all forms...