If/ else if statements to show and hide
You're right, it is a bit repetitive. I believe you could boil it down to the following:

var door = id2 + id3.substr(1);
$("g" + door).show().siblings("g:not(#BG," + id + ")").hide();


or even:

$("g" + id2 + id3.substr(1)).show().siblings("g:not(#BG," + id + ")").hide();


ALSO if you change:

var doorColorChoice = String($('input[name=radiosColor]:checked', '#myFormFront').val());
var id3 = String("#" + doorColorChoice);


to

var id3 = String($('input[name=radiosColor]:checked', '#myFormFront').val());


you could have:

$("g" + id2 + id3).show().siblings("g:not(#BG," + id + ")").hide();


(provided the rest of your code doesn't need the "#" (hash) in id3. That would be faster than using substr)