Conditional Database View of Postgresql
It's not exactly clear how the one or the two table is to be chosen but something like this should work (I assume that the check_poll table has a single row always):

SELECT
    COALESCE(p.name, u.name) AS name,
    COALESCE(p.size, u.size) AS size
FROM check_poll AS c
  CROSS JOIN user_edit_table AS u 
  LEFT JOIN poll_one AS p //I wan to make this conditional
    ON p.id = u.id
WHERE c.poll = 1        -- whatever shows which poll table to choose

UNION ALL

SELECT
    -- same list
FROM check_poll AS c
  CROSS JOIN user_edit_table u 
  LEFT JOIN poll_two p 
    ON p.id = u.id
WHERE c.poll = 2 ;


or even combine the two subqueries in one:

SELECT
    COALESCE(p1.name, p2.name, u.name) AS name,
    COALESCE(p1.size, p2.size, u.size) AS size
FROM check_poll AS c
  CROSS JOIN user_edit_table AS u 
  LEFT JOIN poll_one AS p1 
    ON  p1.id = u.id
    AND c.poll = 1 
  LEFT JOIN poll_two AS p2 
    ON  p2.id = u.id
    AND c.poll = 2 ;