The reason for this is indeed related to the column being a InputField. Basically what's happening is when you click on the cell (of the InputField) you are applying a selection to the table to filter for rows with that InputField value. This can be confusing when you first create your InputField and your values are likely all blank.
Not a great work around, but how I've done this in the past is to place a transparent text box on top of the table which is nearly the width of the input field, and the full height of the table.This allows the user to click that TINY little blue arrow to go into the InputField without accidentally applying a filter. This is not perfect since you still have to deal with an additional object floating on top of the table, plus there are still tiny slivers of a few pixels on each row where a user could actually still click and apply a filter.