Gravity Forms allows you to create a new WordPress user. Profile Builder Pro allows you to edit those fields in User Meta as long as they have the same name. If the field is multi-select, GF saves the values as ["Value1", "Value2"], Profile Builder does not like this. This snippet will intercept the user creation *AFTER* the meta has been writte…

gravity-profile-builder.php

/**
	 * When a new user is created it goes through the user meta to find entries that
	 * have the format ["Value","Value1"] and replaces it with Value,Value1. GravityForms 
	 * writes multi-select form fields this way and the ProfileBuilder Pro does not understand it,
	 * so we need to replace the entry for PBP to gather what these values are.
	 *
	 * @param  int @user_id - the ID if the user that was just created
	 *
	 * @return void
	 */
	public function gf_pbp_multiselect_fix( $user_id ) {
		$user_meta_fields = get_user_meta( $user_id );
		$gf_regex_identifier = '/\["\w.+"\]/';
		foreach ( $user_meta_fields as $user_meta_field_key => $user_meta_field_value ) {
			if ( is_array( $user_meta_field_value ) &&
				1 === count( $user_meta_field_value ) &&
				preg_match( $gf_regex_identifier, $user_meta_field_value[0] ) ) {
					$gf_regex_target_replace = '/[\[""\]]/';
					$new_value = preg_replace( $gf_regex_target_replace, '', $user_meta_field_value[0] );
					$result = update_user_meta( $user_id, $user_meta_field_key, $new_value );
				if ( WP_DEBUG && $result ) {
					error_log( 'Successfully changed GF meta to ' . $new_value . ' for user ' . $user_id );
				} elseif ( WP_DEBUG && ! $result ) {
					error_log( 'Failed changing GF meta key ' . $user_meta_field_key . ' for user ' . $user_id );
				}
			}
		}
	}

add_action( 'gform_user_registered', 'gf_pbp_multiselect_fix', 10, 1 );