Arduino Libraries: Declaring variables as public?
Classes are used to hide away the complexity of a certain task. The user of the class should not worry about how the library exactly works in the inside, but instead only worry about how it should be used. In many cases directly writing to a member variable can be not only convenient, but hurtful if a wrong value is set. If you instead use a function to set the variable, the author can add code to prevent wrong values from actually being written to the variable. Also there might be some other logic involved, that is not triggered, if you write directly to the variable. So - for the ease of use - the users might want the library to be responsible for this, not themselves.

If you write a library, you have thought about how it should be used. Hiding other ways away is a common way of leading the user through the usage. Ways of usage, that don't go along with the purpose of the library can be hided away to make the correct way clearer. A manufacturer of a saw doesn't give the user instructions how to use the wrong side of the blade, because it doesn't help you with sawing.

This does not mean, that you shouldn't make variables public at all, but only if it makes sense. For example: If you are defining a class, that just represents a point in a coordinate system without hooks to other code, it is totally OK to make the coordinates public. But if you defined the class, so that the point is directly shown on a display, you might want to change the position on the display, whenever one of the coordinates is changed. In this case you can use a set-function to trigger the display update, when a new value was given for the variable.