But he was on probation for an unrelated (i.e., non-First Amendment) charge. I can understand someone being prohibited from possessing firearms (i.e., Second Amendment) while on probation for a violent crime (say, assault and battery), as the two are tangentially related. But there just is no correlation between, in this case, the First Amendment and bank fraud.
prohibitions on “using the internet” are as broad as prohibitions on using the phone or a newspaper.
He used computers and the internet to perpetrate the bank fraud. It's not uncommon to see such restrictions on criminals.