They are definitely teachable. I had to learn them. I won't say I'm great at it, but there was a drastic difference between my effectiveness as a leader early on vs. later on.
Just like technical acumen, you have to start with building low level muscles, and then you build on top of that to develop increasingly complex, integrated skills.
Here's an example breakdown of how to build communication skills from a set of low level skills. I've seen adults (including engineers) improve dramatically with direction and practice:
1. Learning to tell when you are getting angry and building the habit of stepping away instead of escalating
2. Learning to tell when you are reacting in the moment vs. analyzing, and practicing the habit of moving to analysis during tense conversations
3. Learning to stop automatically attributing bad motives to things other people say that you dislike
4. Learning the formula for conflict handling: (1) acknowledging their point, (2) repeating it back with a charitable interpretation, then (3) responding with your point
5. Learning to make exploratory statements and ask questions to establish common understanding
6. Learning to identify and not make overconfident/dismissive/glib statements
Also:
- Exercise regularly
- Maintain a regular sleeping schedule
- Eat healthy (recognize when you are self-medicating with food)
- Make an extra effort to groom yourself (wear cologne, shave daily, clip your nails)