I was taught fixed-do solfège as a child, and only found out a few years ago that there is such a thing as movable-do. I have also been familiar with the A-G letter system for many years, and in my head the two systems were simply two different languages describing the same thing.
When I come across movable-do descriptions of musical concepts, in posts here or in websites and YouTube videos by English speakers, I find it fairly easy to think of do-re-mi... as simply a numbering system, i.e. notes 1-2-3... in a certain key. It's similar to how, if someone says ii-V-I about a song in C, that automatically translates to Dm-G-C in your head, without requiring much thinking.
I have seen many comments online assuming that movable-do is a problem for people from fixed-do cultures, but I can't say that I have experienced this myself. And I assume that any person who has been making music for a long time, or is studying music, would be able to adjust easily. After all, being able to transpose music into another key is a skill that is often needed, and movable-do is a similar concept. It's also similar to the way you translate a barre chord of a certain open-chord-shape on a guitar to the actual chord being played as you move up the neck. People who play a transposing instrument will be even more likely to see the naming of notes as something that is inherently movable.