You said that you have heard the word 'often' pronounced with and without a 't' sound. It is accepted as correct both ways. It depends on the region. Dalziel (His name is not pronounced as you might expect) From BBC's Dalziel and Pascoe pronounces the 't' in often but I don't. We both have British accents but his is a West country accent. Most peope will drop the 't' in often . Without knowing how you speak , I'd suggest that you drop the 't' and concur with the majority.
There are many different English accents. There are broadly speaking, around 12 clearly identifiable accents in Britain. There's more diversity within Britain than outside Britain. The most extreme accents being Rab-C Nesbitfrom Glasgow (Search You-Tube) and the Newcastle accent from the North East of England.
If you would like to learn any of these accents then I could offer to teach you from a book called "Accents for actors"
A lot of times, people who enunciate the 't' in 'often' are attempting to appear smart or educated. It's an intentional enunciation. "Offen" is generally accepted as the right way to say it, though, so the attempted show of intelligence strikes one as ironic.
That's true I hear that in my work a lot of more than in the streets.
Your thorough explanation is really interesting especially for people [ like me, for instance ] who don`t have much knowledge regarding the diverse accents in English. However, how do professors from Cambridge or Oxford pronounce this word - often ?