Rock on! I love these kind of discussions.
I don't think you need any training to experience an emotional reaction to certain colours. I really, really don't. I had a recent conversation with my sister in law (who is child who has had no artistic or psychological training of almost any kind) about the colours she loves and the colours she hates - how she recently dared to buy a yellow shirt for the first time, even though my mother in law hates yellow, and how she hates red, even though red is my favorite colour. How both her and I and my mother in law don't like pink. We talked about the broad variety of reds, and how some are warm and others are cold. How some reds make her feel stressed or angry, while for me some reds make me feel powerful. My husband piped in and said "red is passionate." "Or like blood." You can have that conversation with almost anyone of any culture, of almost any age. Colour psychology, as far as I'm concerned is a real science. It is extremely rare to find someone who doesn't have a bias toward certain colours or to find a culture where colours aren't assigned relationships to emotions - colours for mourning, colours for celebration, colours for neutral spaces.
Here's and example using the Rothko painting I had the most immediate emotional response to:

What emotional response do you have to these colours? And to go deeper, what does your response remind you of in your own life?
This is not to say you have to like the painting. I don't
like this painting, even on the small scale of looking at it on a screen it makes me uncomfortable and I wouldn't want to hang it in my home (it's 80.0 in × 69.1 in) but I can't deny that it elicits specific and strong emotions from me and prompted a memory of some of my darkest (not pun intended) times. I do contend that, universally if you showed this painting to various people, and asked them these two questions, you'd get a myriad of different, fascinating and very personal answers, but that the majority of people would be able to answer both questions. More interestingly, I think their responses would change day to day, and that's interesting too. If you read about Rothko, his desire was to be universal, not to exclude, which is the opposite of a circle jerk. If you look at the chapel Paul posts about, it looks like a suitable place for people of any belief system, including an atheist like myself, to go a mourn (though I shudder to think of anyone getting married there even thought the chapel's website lists it as an option).
On the other hand, we can have a conversation about whether Rothko's work is pretentious, or if abstract expressionism more broadly is pretentious. What can I say... all art, on some levels is about navel gazing, and this art form is about looking inward more so than many others. It can be pretentious, self absorbed and self serving to look inward for sure. Reversely it can be meditative and therapeutic. I can't deny that when I go to an art gallery, I prefer to whizz past most of the abstract pieces because they fail to engage me in an immediate way. I feel embarrassed to get into a meditative state in a public place
because it looks so self absorbed. When I turn to art, I'm not typically looking to be reminded of myself, but rather to be reminded of my connection to others, which is why my preference is to performance and sitting in audiences. But what floats my boat is different than what floats another person's boat.