Due to having a thesis advisor,Y, that did not reply my e-mails at the beginning of the process of choosing a topic, I had approached to another professor in the department, X to change my advisor. She rejected my request as saying she was too busy. (But I somehow feel this as an excuse because maybe she did not want to takeover Y's student, as they are quite close friends in the deparment..) We had continued with advisor Y, but it's time to determine my jury members. The professor X's research topic was too close that of mine and my thesis, would it be awkward to invite her? I know my advisor Y will invite her and he mentioned that once (plus he doesn't know of course that once I approached her to change my advisor..). I think X would accept being my jury member but would it be a weird situation to call her, as once she rejected being my new advisor..
I think X would accept being my jury member but would it be a weird situation to call her, as once she rejected being my new advisor..
I don't think it would be weird. This is exactly why people usually decline "politely" (as in: "I'm too busy" rather than "I don't want to") - it leaves the door open for future interactions.
I think if your advisor suggested her, and you think she is a good jury member, you can definitely approach her (or have your advisor approach her, depending on how this is commonly done at your institution).
As a sidenote:
plus he doesn't know of course that once I approached her to change my advisor..
Depending on the conversation you had with X, I wouldn't necessarily rely on this being the case. Have you asked her explicitly about keeping your request confidential? Otherwise I would assume that standard operating procedure is to talk to your current advisor about it before answering, especially if they are good friends.