Chrome Developer Tools allows this. There's a button in the Source tab to deactivate breakpoints from debug statements. The button looks like an arrow cut in half.
I believe the reason you and the person you're replying to disagree, is that it works for existing debugger statements, but seemingly doesn't work for debugger statements injected after you toggle the flag.
The "disable breakpoints" button is seemingly performing a one-time imperative action on toggle (maybe "find all the breakpoints + debugger statements in existing loaded code, and patch/unpatch them") rather than being a declarative state-change in the system (i.e. "disable this tab's access to the debugger/breakpoint logic itself").
