There has been no change in Denmark's Schengen membership. All visas are valid as before, and a Schengen visa to Denmark, Sweden, Germany or any other Schengen country will remain valid - also in Denmark!

There are no passport control at intra-schengen borders, nor any police directly at any land borders. There are no identity checks at any intra-schengen borders. The only passport and identity controls will be at international airports and ports at arrival of aircrafts and ships from non-schengen countries such as USA, Canada, Ireland, UK, Russia, Turkey etc., such as at any other non-schengen border.

Denmark has increased the customs controls, roughly to the level of Sweden (who has customs officers present at all borders 24/7) and Germany.
Denmark has increased the number of customs officers with 11 (eleven!) as an increased effort to stop drug and weapons trafficking and other illegal activities. There are no permanent customs checks at any intra-schengen borders, only random checks.

The whole story is blown out of proportions.