It looks like fungal infection and the beginning of shell rot, since you said it's soft
when you press on it. The best remedy is to go to a vet and get silver sulfadiazine
cream (if I spell it correctly). You need to dry dock the turtle when applying the
cream. The vet will let you know the right procedure. I don't think it'll matter if
the vet is an exotic animal vet. All vets should have basic knowledge about the
main animal groups.
Cheaper and not really correct method is to use a wide spectrum antifungal cream
for humans, for example the cream to cure athlete's foot. What you do is dry the
turtle, then clean the infected area with betadine and let dry for about 15 minutes.
Next, you apply the cream and keep the turtle in a dry place (dry docking) for
a day. At night, clean the cream thoroughly first before putting the turtle back
into the tank. You need to clean the tank thoroughly to avoid reinfection. Do
this for several days until no more white patches.
To avoid this, you need to make sure the turtles can dry out several times
daily while basking. Drying the shell makes fungus can't grow.
I've done what I described above, but my turtle's shell wasn't soft. In the end,
the shell shedded revealing healthy shell underneath. If anyone thinks this is
"dangerous" for the turtle, feel free to comment.
