Hey Nieta,
For example these kind of custom field 'avatar', 'header', 'editor' and other shouldn't show in advanced search by default.
What i fix for that user site which already included in the current latest version of Easysocial.
If you do not want those field searchable in Advanced search, you have to disable this 'searchable' option from your site backend > Easysocial > Custom field > workflow > edit your user workflow > edit the custom field > disable 'searchable' setting (
http://take.ms/X3BR3)
If the issue still persists, can you start a new thread on our forum and provide us with your site details so we can better have a check.