The file is: "themes/classic/templates/customer/_partials/customer-form.tpl" (or your custom theme folder) but there is a loop going through the "formfields" which are defined somewhere and pushed in that template. You could go through them and identify their names and put {if} condition not to display them, something like (but you need to identify the key and name of the fields yourself):
{foreach from=$formFields item="field"}
{if $field.name ne "password" && $field.name ne "birthday"}
{block "form_field"}
{form_field field=$field}
{/block}
{/if}
{/foreach}