Can solid soap cause a drain blockage?
Yes, there is some truth to this. Most solid soaps (with a few exceptions like Dove) are made with animal fats which cause the ingredients to bind and become solid.
When a bar of soap is used in hot water, a little bit dissolves and goes down the drain. As long as the pipes are sloped downward and moving freely, the soap won't cause a problem.
But if there is a "belly" in the pipe (or a place where water pools), then soap, grease, hair, and everything else in the drain congregates there.
This is typically where soap and grease solidify (or "congeal"), causing blockages. In fact, a soap blockage is often mistaken for a grease blockage because they look so similar.
To prevent a soap blockage, your best bet is to use liquid soap or body wash because they don't use animal fat to solidify their product.