If someone of sufficient expertise decides to hack you and take your banking info, they will, just like if someone decides to rob you on the street, they will. We assume there are vulnerabilities in any piece of software as big as Firefox. Your security depends on not being a particularly tempting individual target for highly skilled attackers and staying up-to-date enough to avoid mass automated attacks, and those factors depend on relative risks that can't even be objectively measured.
Edit/PS: I am also confident that the government would not insert back doors that are likely to be found by criminals, because those vulnerabilities would be exploited by foreign governments and would hurt U.S. commercial interests, which I imagine is the only kind of mistake that would result in Congress taking drastic punitive action (slashing budgets, reducing autonomy, increasing oversight) towards an intelligence agency.