Canada

but it seems to me that employers are free to choose whomever they like.

Absolutely. Hence the election process, literally allowing the employer to elect which employee they wish to hire.

Choosing someone on the basis of their refusal to join the union seems like a great way to start a walkout among your other unionized staff though.

The question wasn't about refusal to join a union, the question was directed to those who hire based on union membership. e.g. the people who always vote for the candidate who belongs to the Liberal union, or the Conservative union, no matter who the actual person trying to get the job is – as opposed to evaluating the potential hires based on their merits as a potential employee.

If you are building a deck, and one guy belongs to the United Steelworkers, and the other belongs to OSPE (engineering union), do you automatically believe that one union always produces better employees every single time? Or do you look at the actual people and try and evaluate which one will do a better job? Now, the question was directed at the first group. Is there something about one of those unions that means it will always present the best employees for deck building?