To me they're just numbers, -1, -5, or -10 at the most loss with each source has a 5 minute cooldown on how often they can trigger again. All of which can be recuperated with a single daily quest that gains +125 completely erasing whatever you did that day and then some. You have to really go out of your way to make them hate you and some players enjoy doing that to see the responses and messages that companions would not otherwise say unless brought very low. Even if you get them to a point where they leave you, it has a cooldown period where it resets and can call them back a day later, you cannot lose them permanently no matter how low their rapport drops.
However some seem to really take it hard when negative rapport happens, it can trigger them when an NPC gives a scripted response to "not liking" your actions. I like to understand why, I've never put them away to complete an action whether its stealing and murdering while Bastian or Isobel is with me, I gleefully pluck the wings of butterflies in Mirri's face, her response puts a smile on my face. Ember is meh, her "ooh shiny" or maniacal laughter is way more entertaining, she wants to pick on someone else after killing a boss let's go!