So for those I didn’t just scare away, here’s how to enable SVG uploads in WordPress.
Locate the functions.php file in your theme, and add this code to the bottom of the file. This will add SVGs to the accepted list of file types.
$new_filetypes = array();
$new_filetypes['svg'] = 'image/svg+xml';
$file_types = array_merge($file_types, $new_filetypes );
Now if you try to upload an SVG you will likely still get an error stating your image is not an acceptable file type. This is because all SVGs you upload must include the xml declaration as the first line in your SVG file.
<?xml version="1.0" encoding="utf-8"?>
After adding that line you should be able to upload SVGs.