When exporting constituency codes for a list that includes both records with expired (ones with end dates that have past) and current codes (those with future end dates or no end dates) there is no way to tell the export to only export current codes. This would be a very helpful feature.
Yes! Why is anything "inactive" from the database even showing in the web view?
Related to the above comment, when you're in a database view query you can simply choose the date to field as blank/not blank to get the records with that constituent code that are current/former respectively. But I agree, right now it's not possible to select current/former constituent codes in web view Lists, which will be necessary in order to switch all of our processes from the database view to the web view.
The current work around is to group all the records with current constituencies and export from query. Then you can match up the records in your export with any record that showed up in the query. (Using VLOOKUP or similar tools)