Short answer: yes. The word list behind the original game is American, so FAVOR, COLOR, FIBER and TIRE can all turn up as answers, and the British and Australian forms of those words are not what the board is looking for.
If you learned to spell in Britain, Australia, Ireland, New Zealand, Canada or India, this is not a small annoyance. It is the difference between losing on your own knowledge and losing on somebody else's dictionary.
Where it actually bites
There are two separate problems and they are usually run together.
Guesses being refused. You type FAVOUR and the board tells you it is not a word. It is a word. This one is easy to fix — accept both spellings — and most alternatives do.
The answer being a variant. The word of the day is FAVOR, you spend three guesses on FAVOUR-shaped words, and you lose. Accepting both spellings does not fix this. Somebody still has to type the spelling that looks wrong to them, and be told they were right to.
Why we do it differently
Two decisions, and the second is the one that matters.
Guesses follow your dictionary. Pick US, UK or Australian and the accept list follows. FAVOUR, COLOUR, TRAVELLED and CENTRE are all valid guesses on the British setting, and both ‑ISE and ‑IZE endings are accepted because British English genuinely uses both.
The shared daily answer is never a variant word at all. Any word whose spelling changes between regions is excluded from the daily pool outright. That is stronger than accepting both forms: there is no day on which your spelling is the wrong one, because the word of the day is a word that is spelled the same everywhere.
The daily stays one shared word worldwide, which is most of the point of a daily puzzle — you and everybody else are solving the same thing. The region setting decides what you are allowed to type, which is where it belongs.
If you just want to play in your own spelling
There is a British page and an Australian one. Both draw their practice words from that region's list, so nothing you are asked to guess will look wrong to you.
The ones that catch people out
| American | British and Australian |
|---|---|
| FAVOR, COLOR, HONOR | FAVOUR, COLOUR, HONOUR |
| CENTER, THEATER, FIBER | CENTRE, THEATRE, FIBRE |
| TRAVELED, MODELING | TRAVELLED, MODELLING |
| DEFENSE, LICENSE | DEFENCE, LICENCE |
| GRAY | GREY |
GRAY and GREY are the cruel one — both are valid words in both places, which means neither list can rule the other out, and you can spend two guesses discovering which one the board wants.