sets-file-type-for-bp-profile.php

<?php
/**
 * Sets the file types for upload bp profile avatar.
 *
 * @param array  $exts extensions.
 * @param string $type attachment type.
 *
 * @return array
 */
function wbcom_set_file_type_for_bp_profile_avatar( $exts, $type ) {

	if ( 'avatar' !== $type ) {
		return $exts;
	}

	$exts = array( 'jpeg', 'png' );// Add your own file types.

	return $exts;
}

add_filter( 'bp_attachments_get_allowed_types', 'wbcom_set_file_type_for_bp_profile_avatar', 10, 2 );