By 1948, the year of White’s death, anti communist hysteria was in full swing, and the State Department was the focus of suspicion for the witch hunters.
White’s wartime closeness to the USSR (which, the fact that America was allied to the Soviets, was hardly surprising) came under close scrutiny and there does appear to be circumstantial evidence to suggest that he may have been a Soviet agent. However, it is not the job of historians to give the nod to vague or generalised ‘possibilities’, but to find solid evidence. In this case it seems more likely that White, who with Keynes was the architect of institutions that gave global capitalism it’s longest and most profitable epoch ever, was anything but a communist, he was simply a social democrat (which in the fevered climate of the late 1940s might have amounted to the same thing).
There were indeed Soviet spies in America, but White was unlikely to have been one of them.