Having just spent most of the last 7 months in Thailand (including 4+ weeks in Phuket), I feel safe everywhere. I wouldn't go to the deep south. With the low cost carriers, there is no reason to anyway.

Areas with the problems have virtually no tourists. The gov't won't accept threats to its' tourist income.

The problems there although reported as religious in nature... I suspect to be more political and based on the high level of corruption in the deep south...
... but then I'm a naive Canadian, what to I know.