How do I export variable columns to a CSV file using PHP?

Yes it is. You have to make a form where the user selects the fields they want to export, I'm thinking in a checkbox list where you list all the posible database fields the can get, and then create the query according the user selection. Ej:

<form action="" method="post">
    <label><input name="fields[]" type="checkbox" value="name"> Username</label>
    <label><input name="fields[]" type="checkbox" value="birthdate"> Birthdate</label>
</form>

And then on the server side create the database query.

$sql = "SELECT `". implode("`, `", $_POST["fields"]) ."` FROM db_table";

Hope this help.