When designing web content for people with color blindness, you don't need to convert all your images to black and white or remove them entirely. In fact, you may not need to change your images at all. Here's the key: make sure color is not the only method of conveying important information.
Most of the time, people with color blindness have no problem with images. The fact that an image contains colors they cannot perceive isn't necessarily a problem for them. It can be nice to see colors, but visitors can understand the image perfectly well even if all colors were removed. However, if the purpose of publishing an image is to convey a message using the colors in that image, then you must provide an alternative. For example, if an image shows bus routes where the routes are distinguished only by the color of the lines, you'll need to add annotations or symbols to the graphic itself (and provide appropriate alt text) or provide an additional explanation, such as a written description of the bus route.
By the way, people with color blindness aren't the only ones who benefit from this technique. People who are blind and also cannot distinguish colors, and older adults, will also benefit.
In the images below, you can see a small illustration of how people with different vision conditions see a website.
Website with no vision impairment
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A person with early-stage glaucoma
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A person with partial color blindness (red-green)
A person with complete color blindness (monochromacy)
A person with early macular degeneration
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A person with severe cataracts
A person with early diabetic retinopathy
A person with early retinitis pigmentosa