To me, pure sci-fi is about the characters using technology derived from current day scientific knowledge (spacecraft, robotics, directed energy weapons, etc...)
This is where we differ the technology itself is unimportant to me in the science fiction I enjoy, it's the impact on humanity or the individual that makes something sci-fi to me.
Take directed energy weapons, they just represent a special effect to replace a missile, their usage in star trek is just the same as in a western, they don't generally represent fundamental change or scientific thinking, they just provide a veneer of science Phaser = pistol, Communicator = radio.
With a few exceptions, Star Trek isn't really interested in the ramification of progress, it just happens in the background.
The transporter is an example of this - in Star Trek, it's usage is just a way of cutting budget. A sci-fi story about a transporter would explore issues like the nation state (do identities blur when you can live on one side of the world and work on the other, does easy availability lead to overcrowding in pleasant areas and rich countries?), the family (does the extended family really become extended?) and so on.
A measure of man is I think the best example of Sci-fi in that vein because it's not a story about a android, it's a story about life and values and worth. Is Data a person? what is a person?
That's not to say I don't enjoy the other types of sci-fi stories just that I wouldn't think of them as "pure" sci-fi.
I'm kinda similar to what I think pure sci-fi is. I like it when it is technology and or a discovery or exploration of the unknown (deep space for example) and it's impact on society and that impact reveals something about us in a new way. That's what I look for and love.