This is a great question! There is no official clarification about this interaction so we are here combining expansions "at our own risk".
In this situation, I would think of these two possible courses of action, according to the way you apply the rules:
a) Strict mode: you only may open a gift after drawing one tile as if in the base game.
In this case, you can only open a gift if you draw one regular tile as usual. This means that using an abbey, a German castle, a Halfling or a tile purchased in a bazaar prevent you from opening a gift.
b) Loose mode: you may open a gift after drawing a tile if there is not interference between mechanics.
In this case, you may always open a gift but you may have some restrictions regarding the "Take 2" gift card. This means that using an abbey, a German castle, a Halfling or a tile purchased in a bazaar would prevent you from opening a "Take 2" gift, since it would not make sense, since you have already a tile to place you haven't drawn. There is an edge case here regarding the purchased tile: if you cannot placed it, you would discard it and draw a new tile, so you would be allowed to open a "Take 2" gift.
I prefer the loose mode, since it provides a more flexible approach by allowing to open a gift always but restricting the "Take 2" gift to those case where it makes sense.
Additionally, the "Take 2" gift also may have a conflict with The Fortune Teller. In this case, I would need to decide between two options:
a) Choosing between the two mechanics when drawing a tile
b) Combining them by using the gift card to draw +1 card in addition to the ones granted by your fortune tellers.
But again, you will have to house rule this decision for the time being.
What do you think?