Something else: Those who encourage others to opt against the covid vaccine, claiming (among other things) the process was rushed, or the risk of some severe adverse reaction is significant, are indeed anti-vaxxers.
It doesn't matter if they or their kids have been vaccinated for other things. Just like those who were 'only' opposed to or concerned about parts of the MMR vaccine, the end-goal is the same: To discourage a given vaccination.
"I'm not against vaccines, I'm just against this one" is not the scientific stance many seem to believe it is.
Further, standing behind the Great Barrington Declaration which aims for herd immunity 'naturally' over vaccinations is an anti-vax approach.
Also: "I'm not a pandemic denier! I just believe the true scope of infections and/or death has been inflated and that many known ways to mitigate the spread of the virus, like universal mask-wearing and targeted lockdowns, are actually not effective at all!"
When people sincerely wonder whether this sort of abuse of athletes might actually just be "tough coaching," you begin to understand how broken the culture is.
As someone who has been Confirmed into the Roman Catholic Church and who wishes people a Merry Christmas without any agenda beyond wishing them well, I'd suggest that non-Christians not take up this selfish and childish fight on behalf of Christians, many who want no part of it.
If someone wishes you well in any manner this Christmas and you take offence to their effort, it's you who has the problem.
If you are (ostensibly) wishing someone well with the prime motivation of 'owning' some perceived enemy, you should prob reflect on the faith a bit more.
If Dawkins thinks "Happy Holidays" offends or disrespects Christianity, wait until he finds out how Christians feel about the things atheists - especially the most militant - say about their religion and beliefs.