Whether you can ask:
Should I bring this up to my boss and try to get a different computer? Or should I just try my best to learn Mac, but suffer from being unproductive for a while?
Yes, you can ask your boss to provide you with a different laptop / computer / OS to work with, as long as that meets your work criteria.
At best, you'll get a replacement system which which you're comfortable with.
At worst, you'll be refused (companies have their own guidelines for providing systems - tech support is one of them) and you'll fall back into the second part, "learn (how to use) Mac, but suffer from being unproductive for a while". However, at least then your boss will know you're trying to learn your ways around the new OS and can have some delays expected/ planned for your work assignments delivery.
However, my suggestion will be: Get familiar with the new OS. It'll be a new learning, and given that you're familiar with Linux, learning your ways around Mac will not be too difficult and time consuming IRL.
I don't want to stir the pot, but I'm not sure how I can do my work when I can barely work with the operating system.
Just the way you learnt operating Windows, or Linux, or your Android /iOS smartphone - practice and learn.
The best part is: This way you'll convey your willingness to explore, learn and adapt to new things, which is a very positive sign for you as an individual and your career.
As they say: If you never do anything new, you'll never get anything more than what you've already got.