Yes and no. On one hand, phobias are legitimate mental disorders, which can be very difficult and unpleasant to try to overcome. That should be respected, as much as is possible, and lumping such people in with anti-vaxxers does not give them that respect (though a great many anti-vaxxers are afraid, and as tempting as it is to berate them for being stupid, being sympathetic to their fears is probably going to be more productive).
On the other hand, the pandemic is a very serious issue, and if there were ever going to be a time to confront his fears, this was it. I'm quite certain this guy had the option to seek out the necessary resources to support him through such an effort (whether formal therapy or just friends/family to comfort and encourage him as needed), so holding him accountable for his decision not to is not unreasonable. I'm saying that from a place of considerable privilege, given that needles don't bother me in the slightest (I routinely stare right at them), but he nevertheless did have the option of trying to overcome his phobia.
No this is plain black and white. You're just flat out ignorant and wrong. It is completely 100% unreasonable to blame this guy at all for being scared of something.