In Canada, there is a variation of chess in which king and queen are swapped from the normal starting position. However, some argue this makes no difference. Canadians are split. So the question is:
Does swapping king/queen from the onset affect the game?
This does not make any difference. Exchanging the positions of king and queen on both sides just corresponds to mirroring the whole game horizontally. Thus they are equivalent.
If both sides swap queen and king at the beginning, it is obviously still the same game, only mirrored in the middle. All theory would still be valid.
Practically, it would be incredibly annoying to anybody intimately familiar with the normal setup. Even more so than the common quarter turn of the board, where all the squares have the wrong colour.
If only one side swaps king and queen this would probably benefit white. White is usually the one who can open up lines first and in this chess version the black king would already be on the same line as the white queen.
Clearly there are trivial differences. Instead of playing e4 for a sharp game, White would play d4. (See Ignaz' answer)
It would also be no different than allowing Black to move first with a normal setup. So no, it would make no difference.
It can make a difference with respect to castling. As others have said, we just have a mirror of the regular startup, so a regular e4 becomes d4 and so on.
That leaves the question what happens with castling? If this is just mirrored as well, then indeed there is no theoretical difference. So in this setup, what are the rules for castling?
There may still be a practical difference, because one has to mirror their usual opening setups or and/or middlegame plans. Apart from that, it will be the exact same game.
No, there is no difference at all theoretically since the game is mirrored, so the relation between the pieces is still the same. However, there is a practical difference. For players used to playing normal chess, they might instinctively play Nf3, but now, since the board is reversed, then he/she is playing Van Geet's opening, which is sub-optimal.
