If you want to avoid being trapped by Jewish geography, you have to know your enemy and consider your answers in advance. When caught by surprise or without a prepared answer, you will say precisely what you will regret later. One such conversation is profiled here.
So what topics are most common?
Did you grow up religious?
Were your parents religious?
How and where you became religious.
Where your family is from. (before America, England, wherever)
The Jewish community (or lack thereof) in the place where you grew up.
The Jewish history of the places where you've lived. (You should learn about this.)
Jews who live in or near the places you have lived.
A sneaky tactic: your family members' names, either first or last. (Example: I had a Shabbat dinner ice-breaker "What were your grandparents' names?" meaning first names and how "funny" and old lady-ish/man-ish they are.)
Questions about survivors in your family or what your family did during "the war."
Where some physical trait comes from. (Example: "Where does your red hair come from?" or "Green eyes are so rare in Jews!" If you learn about Jewish communities worldwide, you will inevitably find a culture that has the trait. For instance, my red hair comes from German heritage, which can certainly be Jewish.)
If you are an ethnic minority, they'll could come straight out and ask if you converted or if your mother is Jewish.
How do you get out of these conversation traps? If you have baal teshuva-like answers (as I do to many questions), you can be honest if you want to and the person may believe you were born Jewish. Maybe you choose to give short, non-committal answers...or maybe even to flat-out lie. Personally, I wouldn't consider it a "bad" lie to give the "correct" answer to someone who is being pushy and isn't taking the polite answers. Halachic opinions may vary. Another technique: throw out the "really interesting" facts in your story as early as possible to sidetrack the conversation. For example, I can usually derail any conversation by stating that the "Jewish boyfriend" who started me down this path is Scottish. That leads into shock that there are Jews in Scotland and a discussion about the Scottish community. This is why you should learn a lot of Jewish history and the status of any current community that has even the vaguest connection to you. It allows you to deflect the conversation away from you without looking like that's what you're doing.
What are some polite ways to decline these kinds of questions? Feel free to add your suggestions to the comments!
"I'd rather not discuss that right now." Then change the topic.
"That's kind of private." (This one can come off snooty or rude, so be careful. However, it can be a "gentle" warning to back off when someone is actually being rude or inappropriate)
"That's not something I like to discuss [in public]." (Optional: "Maybe we can discuss it in private later?" Or "maybe we can step over here and talk about it in private?")
"I don't like to dwell on the past." Then change the topic.
"I don't think this is the place to discuss that." (Again, use sparingly and only when really deserved.)
Turn the question around on the person or ask them a different question. (Example: Take a bite of food, make a surprised smile, and say "I'm sorry, but wow, this egg salad is amazing, what's in it??")
Turn the question around to ask a third person something. Preferably, don't deflect the question to an unsuspecting stranger who might be in the same boat! Alternatively, you could open a question/topic to the group as a whole. (Example: "That's a great question! What do you guys think?")
Excuse yourself to the bathroom, to refill your drink, or to get more food.
If you're feeling fiesty, you can give a TMI answer that scares the person away from any other personal questions. Beware of this backfiring, especially later gossip.
My personal favorite if someone is giving "advice" or chastising you for something dumb: "Thank you for your input." You can choose to add things like "I'll keep it in mind" or "I'll take it into consideration" as the situation warrants. Smile, and then walk away. This takes a lot of self-control, but it rarely burns bridges you may want later. That is particularly important when it is a stranger...who may turn out to be your rabbi's mother or your boss' husband.
However, this whole post, and the assumptions behind it, beg the question why converts feel the need to hide their religious history. That is a post for another day soon.