Should I shrink my database?
I recall that the rule of thumb used to be "never shrink databases". Does it apply in this case?


Yes. Dont touch that shrink button - Its a general rule and a very very sound advice from many renowned SQL Server Gurus - Paul Randal, Brent Ozar, Mike Walsh, Gail Shaw and many more.


  The database is still in use, and still somewhat growing, but I do not think it will grow to use all 1.2Tb in the next 3-5 years.


You have to be 1000% sure about your assumption that its growing but wont grow to this size in your proposed 3-5 years (its a 2 year difference as well :-)). 

still somewhat growing -->You really need to find out at what pace it is growing. Are you doing database growth tracking by collecting the data growth over your complete business cycle ?

Now a days, data is what keeps the companies in business and databases are meant to grow.

Think about it - what are you going to do with the disk space that you gain from shrinking the database ? 

Concentrate on more important areas of optimization as @AaronBertrand suggests.

Even if you decide to shrink , I would suggest you to 


Do a reorg/rebuild and update stats after the nasty shrink operation
Take a full backup to be safe with all the indexes intact.
Adjust your auto-growth settings to not allow the auto-growth events kick off more frequently.


Edit

After OP's comments ---

Then go for it ... since you are or will be moving away data from SQL Server to PostgreSql. But do the post steps once as I mentioned in my answer - once you do the shrink operation. Also, use DBCC SHRINKFILE as you have more control of what you are shrinking as opposed to DBCC SHRINKDATABASE.