Look, ma, no loops!

But seriously, if you were concerned about performance I don't think it's a problem of nested loops per se, $.grep in the loop concerns me much more. Especially since you're doing basically the same grep over and over!

After grep, neither item.parent_id nor i are used again. Looks like we can just cycle through all widgets in one $.grep, and that's exactly what we're going to do.

Also, what you're doing with item.widget_key begs for a switch statement - or, at least, having those radiobutton and dropdown typed twice bugs me and begs for a well-placed typo to cause lots of frustration.

I'm not sure I understand exactly what you do with default_next_step, so correctNextStep probably needs some refinement (like, what if next_step - 1 is not a valid forum section index either?) but the code is supposed to work exactly the same as yours. (or not work, hard to say without test cases:D)

const inArray = (needle, haystack) => (-1 != haystack.indexOf(needle));
const parseIntIfDefined = (item) => ('undefined' === typeof(item) ? null : parseInt(item));

const applyFormSectionIdsToControls = function(formSections) {
  if (!formSections.length) return;

  const formSectionIds = formSections.map((section) => parseInt(section.id));
  const correctNextStep = (nextStep) => {
    if (inArray(nextStep, formSectionIds)) return nextStep;
    return formSectionIds[nextStep - 1];
  };

  $.grep(application_widgets, (item) => {
    if (!inArray(parseInt(item.parent_id), formSectionIds)) return;

    switch (item.widget_key) {
      case 'nextbutton':
        const defaultNextStep = parseIntIfDefined(item.settings.default_next_step);
        if (defaultNextStep) {
          item.settings.default_next_step = correctNextStep(defaultNextStep);
        }
      break;
      case 'radiobuttons':
      case 'dropdown':
        item.settings.answers.map(
          (answer) => answer.next_step = correctNextStep(parseInt(answer.next_step))
        );
      break;
    }
  });
}