One way of doing this in MapInfo Pro is by using the MapBasic Window:
1: Open the MapBasic window thru Options > Show MapBasic window
2: Change the order of the column of one of your tables thru Table > Maintenance > Table Structure
Now notice that the MapBasic statement for reordering your columns has been added to the MapBasic window.
3a. Change the name of the table in the statement to match the next table and hit Enter. This will reorder the columns of that table, too.
3b. Or change the name of the table in the statement to "TableInfo(1,1)". This will reorder the columns of the first table in the list of tables kept by MapInfo Pro.
Note that when you reorder or change the table structure of a table, the table is currently put to the end of this list. You can use this to reorder the structure of several tables, simply by hitting Enter for this statement as many times as you have tables that must be reordered.