Is there a way to have an item be visible on a website and not allow customers to order?

Not in SC(A). There are some fields on item records (don't show price, and No Price Message) but those are for SiteBuilder.

that's what I thought. Thank you

You can create a customization, perhaps based on the dont show price field or a custom field that hides the add to cart button or displays whatever you like

^ we've done that before. I also wonder if there might be future plans for the Personalized Catalog Views to have view-only items for certain customer categories.

We are exploring this a possible future feature.