Is it possible to avoid breaking on a debugger statement in Chrome?

Download the offending webworker.js file to your local drive, and use a text editor to replace all occurrences of "debugger" with ";".

Then use a Chrome extension to replace the remote resource with your local modified version.

https://chrome.google.com/webstore/detail/resource-override/pkoacgokdfckfpndoffpifphamojphii?hl=en

FYI: I do not endorse the above extension. It was just the first I found via Google.

This answer is for an old Chrome prior to 2021 where we could hack the internals of devtools itself by using devtools-on-devtools:

1. undock devtools into a separate window
2. press the full devtools hotkey - CtrlShifti or ⌘⌥i
3. paste the following code in this new devtools window console and run it

{
  const rx = /\bdebugger\b/y;
  const eventSymbol = SDK.DebuggerModel.Events.DebuggerPaused;
  const original = [...SDK.targetManager._modelListeners.get(eventSymbol)]
    .find(v => v.listener.name === '_debuggerPaused');
  const debuggerModel = SDK.targetManager.models(SDK.DebuggerModel)[0];

  SDK.targetManager.removeModelListener(
    SDK.DebuggerModel,
    eventSymbol,
    original.listener,
    original.thisObject);

  SDK.targetManager.addModelListener(
    SDK.DebuggerModel,
    eventSymbol,
    async function({data}) {
      if (data._debuggerPausedDetails.reason === 'other') {
        const frame = data._debuggerPausedDetails.callFrames[0];
        const code = await frame._script.requestContent();
        let {columnNumber: x, lineNumber: y} = frame._location;
        let pos = 0;
        while (y--)
          pos = code.indexOf('\n', pos) + 1;
        rx.lastIndex = Math.max(0, pos + x);
        if (rx.test(code)) {
          debuggerModel.resume();
          return;
        }
      }
      original.listener.apply(original.thisObject, arguments);
    });
}

Notes:

• You can save this code as a snippet in devtools to run it later.
• To quickly switch docking mode in the main devtools press CtrlShiftD or ⌘⇧D
• Theoretically, it's not that hard to put this code into resources.pak file in Chrome application directory. There are several tools to decompile/build that file so just add the code to any script that has something like SDK.DebuggerModel.Events.DebuggerPaused inside. One can even write a tool that does that automatically on Chrome update.

Right-click the in the gutter on the line with the debugger statement and select "Never pause here".