In the plugin’s folder edit the includes/bp-registration-groups.php file.
I tested this method today and it’s working.
Change this:
<?php $i = 0; $l = 0; ?>
<?php if ( bp_has_groups('type='.$bp_registration_groups_display_order.'&per_page='.groups_get_total_group_count() ) ) : while ( bp_groups() && $l < $bp_registration_groups_number_displayed ) : bp_the_group(); ?>
<?php if ( in_array( bp_get_group_status(), $bp_registration_groups_show_private_groups, true ) ) { ?>
<li class="reg_groups_item">
<input class="reg_groups_group_checkbox" type="checkbox" id="field_reg_groups_<?php echo $i; ?>" name="field_reg_groups[]" value="<?php bp_group_id(); ?>" /><label class="reg_groups_group_label" for="field_reg_groups[]"><?php printf( __( '%s', 'buddypress-registration-groups-1' ), bp_get_group_name() ); ?></label>
<?php $l++; ?>
<?php } ?>
<?php $i++; ?>
<?php endwhile; /* endif; */ ?>
<?php else: ?>
<p class="reg_groups_none"><?php _e( 'No groups are available at this time.', 'buddypress-registration-groups-1' ); ?></p>
<?php endif; ?>
To this:
<select>
<?php $i = 0; $l = 0; ?>
<?php if ( bp_has_groups('type='.$bp_registration_groups_display_order.'&per_page='.groups_get_total_group_count() ) ) : while ( bp_groups() && $l < $bp_registration_groups_number_displayed ) : bp_the_group(); ?>
<?php if ( in_array( bp_get_group_status(), $bp_registration_groups_show_private_groups, true ) ) { ?>
<li class="reg_groups_item">
<option class="reg_groups_group_checkbox" id="field_reg_groups_<?php echo $i; ?>" name="field_reg_groups[]" value="<?php bp_group_id(); ?>"><?php printf( __( '%s', 'buddypress-registration-groups-1' ), bp_get_group_name() ); ?></option>
</li>
<?php $l++; ?>
<?php } ?>
<?php $i++; ?>
<?php endwhile; /* endif; */ ?>
<?php else: ?>
<p class="reg_groups_none"><?php _e( 'No groups are available at this time.', 'buddypress-registration-groups-1' ); ?></p>
<?php endif; ?>
</select>