Perspective popup transparency

Base your css selector on the popup's id.
Ie, you open the popup with this id "foo".
You can add

#popup-foo {
    background: transparent;
}

But I suggest you push things a bit further and use a prefix in that id, so you can apply it to any popup you want.
Let's say you want a way to make popups's background transparent.
Give them an id that starts with 'transparent', ie "transparent_foo".
Now you can use this css:

.ia_popup[id^=popup-transparent] {
    background: transparent;
}

Now any popup with an id that starts with 'transparent' will have a transparent background.
You can even mix styles if you check if the id CONTAINS a special value:

.ia_popup[id*=transparent] {
    background: transparent;
}

.ia_popup[id*=rounded] {
    border-radius: 25%;
}

now if you open a popup with an id that contains "transparent" and "rounded", (ie "rounded_foo_transparent") it will use both styles.

NOTE: As @cmallonee said, this applies styles to the popup only, not its contents.
In some cases, you may need to apply some more styles to the contents as well.
One possibility is to simply add another rule, targeting the body of the popup, to automatically apply that style.
Something like

.ia_popup[id*=rounded] {
    border-radius: 15px;
}

.ia_popup[id*=rounded] .popup-body {
    border-radius: 15px;
}