It would have to be LBJ for signing the 1965 Immigration Act.
But it's hard to say because immigration policies have shifted so dramatically over the past few generations.
For instance, Theodore Roosevelt was not pro-immigration at all. But the policies of 1901-1909 for immigration were de facto open borders (for white immigrants, without illnesses).
So what matters more, his own contempt for "hyphenated Americanism" or the actual policies of his government?
When TR rallied against "hyphenated Americans", he wasn't going against immigration in general. Here is his speech, which is fairly progressive
I stand for straight Americanism unconditioned and unqualified, and I stand against every form of hyphenated Americanism. I do not speak of the hyphen when it is employed as a mere convenience, although personally, I like to avoid its use even in such manner. I speak and condemn its use whenever it represents an effort to form political parties along racial lines or to bring pressure to bear on parties and politicians, not for American purposes, but in the interest of some group of voters of a certain national origin, or of the country from which they or their fathers came.
Americanism is not a matter of creed, birthplace or national descent, but of the soul and of the spirit. If the American has the right stuff in him, I care not a snap of my fingers whether he is Jew or Gentile, Catholic or Protestant. I care not a snap of my fingers whether his ancestors came over in the Mayflower, or whether he was born, or his parents were born, in Germany, Ireland, France, England, Scandinavia, Russia or Italy or any other country. All I ask of the immigrant is that he shall be physically and intellectually fit, of sound character, and eager in good faith to become an American citizen. If the immigrant is of the right kind I am for him, and if the native American* is of the wrong kind I am against him….