First you take "Where's Wally?" (Waldo), then "Harry Potter and the Philosopher's Stone" (Sorcerer's), and now you're going after poor Yooka-Laylee?!? When will you people be satisfied?!?
(I'm just kidding
But really, if you see the alternate spellings enough, you get used to them and then you just automatically adjust. For example, as someone from Australia where we use British English, I read your initial post and was wondering why you included the word "theater" in the list, because when I read it, my mind automatically corrected it and I actually saw "theatre", until I made a conscious effort to look at it and notice the different spelling of the E and R being swapped around. I actually never knew the word was spelled differently in American English until you said it. I did know about the other words you mentioned, but as Crownless mentioned, that's because I see the alternate/American spelling of those words so much that I can read either spellings and it's not jarring at all.