The game tries to make it pretty clear if a dialogue option you are choosing trends towards Paragon or Renegade. Essentially, options that you choose in the bottom left or bottom right may give you Renegade points. Options you choose in the top left or top right may give you Paragon points. Unless, of course, you're under one of the "Investigate" sub-dialogues, in which case all of the dialogue options tend to be different items of inquiry. Okay, maybe it doesn't sound clear when explained, but it becomes quickly apparent after playing a bit.
The image below does a pretty good job of summing up how the dialogue wheel works. I liked this one better but its watermarked to say it doesn't want to be used off-site, so I didn't embed it.
Getting to your question, no, hanging out with certain people does not change your morality unless you had to specifically choose a dialogue option as shown above to do it. If so, the morality change will be immediate and obvious upon finishing the conversation. You won't randomly receive extra renegade or paragon points from previous choices later on in the game.
I can't think of any specific examples where this is the case as far as party members go, but it may well come into play when acquiring war assets. I'm pretty sure my dealings with the Salarians around the 1/3rd mark of the game were such a case. Regardless, you definitely won't affect your morality by accident, as you'll be able to tell what you're doing through the dialogue wheel.