What role does color play in branding and social media graphics?

couldn't agree more, color creates brand identity and evokes feelings, influences decisions, and impacts how people perceive and engage with your product

It's all about the emotions that are triggered when someone sees your branding. Does it make them joyful, sad, hesitant, excited. Colors speak to our emotions.

When it comes down to a demo and it's between you and a competitor, many will pick based on instincts from look and feel.

True that. Color is also one of the toughest things to nail when creating a corporate identity in my opinion and experience as a designer. It needs to be as consistent as possible. However, as a founder of an agile startup I found it hard to keep everything consistent if every channel is evolving so fast. Also the color palette we initially envisioned was not flexible enough that's why are doing a redesign (the second one in the company history). That means you may need to adapt the colors every once in a while if you feel that it does not match the brand or does not allow you to create all the graphics.

Color is an important aspect for brand identity.

I agree with you!

Branding is one thing and being consistent with it is the other thing. The more you can do the later, more it will help :)

Color is the first that your customer notices and they subconsciously try to find what your brand provides. Then they start to associate that color with your brand

Fun fact: Your brain processes colors faster than words. So, choose your brand's color wisely.

I have seen many brands ruin their brand identity by not choosing a brand color palette and fonts. I think you got the answer!