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.
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").