Is there anyone in our times who ONLY wear t'philin made according to the shitta of Rabenu Tam - to the exclusion of "Rashi" t'philin?
No. Anyone who wears Rabbeinu Tam תפילין wears Rashi תפילין as well. This is because doing so would be saying that Rashi is wrong, which is not something anybody is on the level to do in this generation.
The Shulchan Aruch says that wearing Rashi's תפילין is the accepted minhag, and only a very pious person should also wear Rabbeinu Tam's (ש"ע א"ח 34:1). Therefore, only wearing Rabbeinu Tam's תפילין would go against both Rashi and the Shulchan Aruch.