This looks like a caching issue; you seem to be using a plugin (possibly WP Optimize) that minifies your CSS, and it may need to be refreshed so that the styles include the My Calendar stylesheets.
That would make sense in combination with being able to see the styles when logged-in, since it’s common for optimization plugins not to run for logged-in users.
I had thought of that and have tested by disabling the WP Optimize completely, but I am getting the same result. I also disabled all plugins to check if there was a conflict, but that also made no difference. So I am at a loss.
I have now added an alternative calendar to the site that does work with the WP Optimize plugin active, so no need to pursue this issue unless you want to see if it is resolvable. If you should find a solution, let me know, and I will reinstate this plugin. For further information, in case it helps, the site is designed with Oxygen6 and Breakdance plugins. Content is Gutenberg Blocks, so the calendar was added with the shortcode.
I am interested in knowing what’s preventing the styles from rendering, but knowing that you’re using Oxygen and Breakdance is very possibly enough to go on; I know that Oxygen does some unusual things, and Breakdance may, as well.
I can confirm that Oxygen6 was the template for the Header and Footer on the site, but the page was created using Gutenberg Blocks, as indeed was the content for all the pages. So the calendar was added using a shortcode.
When logged in as admin, the calendar displayed correctly, and once the distorted display for visitors was realized, a check for errors using Inspector was carried out. Nothing appeared to be wrong. So whether the issue relates to Oxygen6, blocks, or some combination of the two is difficult to access. I also disabled all other plugins, other that is than Oxygen6 and Breakdance, in case there was a conflict with another plugin, but that had no effect either.