Step 1: Install uBlock Origin on your web browser.
Firefox link / Chrome link
Step 2: Click on the uBlock Origin icon in your browser's toolbar and select the element picker (eyedropper icon).
Step 3: Move your mouse just above the words "random posts" in the Kbin sidebar so that the entire "random posts" box becomes highlighted in red. Click to make a little window appear with the text "##.section.posts" in a little text box.
Step 4: Click the blue "create" button beneath this text box to make the "random posts" section disappear. Repeat the same process with the "random threads" section, where the text box in the little corner window should read "##.section.entries".
Edit: Be aware that trying the same thing with "random magazines" and "active people" will also filter out "active users" and "related magazines" in a magazine's sidebar.
Re-enabling: To re-enable the "random posts" and "random threads" sections after blocking them with uBlock Origin, click the uBlock Origin icon and then click on "disable cosmetic filtering" (slashed eye icon). To disable the sections again, click the same icon again, which should now have a red X over it.
While I have enjoyed the random posts/threads feature as a way to find new, interesting content that I'd otherwise miss, the feature still has the obvious problem of occasionally showing pornographic, prejudiced, or even illegal content without a user's consent. There is to my knowledge no way to disable these sections through either Kbin's user settings or theme settings, which to me seems like something that should be implemented. Maybe the ideal would be a "show / hide" toggle at the top of these sections, hidden by default, with a warning that enabling these features has a small risk of exposing the user to offensive content.