I am red-green colorblind. So certain shades of colors like that I literally can't see. Blue and purple are issues, and certain shades of yellow and green.

In the image above, I cannot really see a difference in the extremes of the legend. The gradient is definitely not helping. I can see the difference when put near each other. Like Mississippi and New Mexico are clearly on opposite sides, but I would not be able to tell you which direction either leaned because I can't see what the legend is showing. Likewise most of the states mean nothing to me since they're part of the gradient itself going towards colors I can't distinguish a direction from. Without the numbers, this map would mean nothing to me.

Simply put, pick colors on opposite sides of the color wheel when trying to show differences like this with gradients and you're more likely to to okay. Don't pick colors that are next to each other. TRhis might as well have been a blue/purple gradient with an extra z-dimension for time or some crap,

It's not gray, almost no one actually sees in greyscale, despite the jokes. It's always just certain shades the eyes can't distinguish differences from.

A good example for other common colors, is peanut butter looks like a shade of like greenish tan or maybe dark khaki, not brown as most people describe it to me.

A decent resource to explain visually for those that can actually see the full range of color: https://enchroma.com/blogs/beyond-color/how-color-blind-see

It looks like going from blue (-20) to white to blue (+20). It could be modified by using a different color palette - for example blue/green, blue/red, yellow/blue. A good indicator is also if the colors are still discernable in grayscale altough this will be pretty much impossible on a divergent color scale unless you add a second identifier such as dots.

As a non colorblind person, I would like to understand how this image could have been modified to include our colorblind brethren.

In general it is a good idea to use colour gradients that monotonically increase (or decrease) in brightness in addition to (or instead of) hue (see here for an in-depth comparison of different colour maps. It's from a Python package, but it shows some interesting plots comparing different colour maps when it comes to brightness vs. hue). This isn't just useful for colour blind people, but also helpful when printing in black-and-white.

If you absolutely have to use a diverging colour map, you might reach most people by using blue as a major component of one, but only one of the two branches (the map in the OP uses blue as a major component of both branches, which is why red/green colour blind people can have a problem with it). That way most colour blind people should be able to distinguish the branches, since blue colour blindness (Tritanopia/Tritanomaly) is much rarer than red (Protanopia/Protanomaly) or green (Deuteranopia/Deuteranomaly) colour blindness.

Apart from that it is also possible to mark information visually in other ways than by colour, e.g. by shapes and patterns, like dotted or dashed lines for line graphs, shaded or dotted areas for bar and area graphs, or different geometric shapes like crosses, diamonds, and circles when plotting individual data points, but that is probably more useful when different sets of data are plotted in the same graph.