When it's white like this, there are usually 3 suspects:
1 - hard water but that does not seem likely from the splotchy pattern
2 - bacterial infection but there would be a lot of pitting. there are a lot of retained scutes, which gives it that appearance but it's likely...
3 - fungus. Grows in random spots or branches out in patterns. It's infectious to other turtles and spreads quickly.

