This Firefox issue is easily fixed by adding title="search" to the input form. Hopefully XenForo will add this tag so that Firefox users no longer see this issue. In the meantime you can install this add-on:
Thank you for reporting this issue, it has now been resolved. We are aiming to include any changes that have been made in a future XF release (2.2.13).
Change log:
Attempt to prevent browsers from autofilling credentials in the find member widget