For a person who is IN the conversion process, there are instances where you would probably have to tell someone that you are converting. If you're a man (or a woman in a non-Orthodox setting), you might be called up to the Torah and have to explain that you're still (four years in, sigh) in the conversion process. A friend had this happen to him at an Orthodox synagogue and he had to, quite embarrassed at the time, decline the gesture even though he was so overwhelmed with love for the white Jews who had not even thought (or kindly knew better not) to question his Jewishness as a person of color.
In the Orthodox community, if you haven't converted, you can't pour/handle non-mevushal (uncooked)wine so if you're at a meal with Jews, you'd have to make sure the wine you're being asked to pour is mevushal (cooked) wine. Oh, man, this has led to many incredibly embarrassing (for me) interactions with converts-in-training. I mean, it's quite hurtful and strange to be told you can't pour/handle non-mevushal wine that you've unwittingly bought your host because you haven't converted yet. The first time this happened, I had no idea what to do. People usually buy mevushal wine when hosting a lot of people. I don't ask people if they were born Jewish, are converting or have converted so if they want to tell me, it's up to them. ("Do's and Don'ts of Talking to Converts"
There's also some issues surrounding holidays, particularly Passover, where you'd want to give your hosts the head's up that you're not Jewish but this is just so they can (sigh) talk to their rabbi and their rabbi can explain that the strange laws do not mean that they can't invite you over for a holiday meal. I know people who haven't been invited at all for any holiday meals during the conversion process because of some misconceptions or differences in how a couple of particular laws are read. Horribly hurtful for the prospective convert again who is trying to learn about these important holidays.
Anyway, I've been meaning to post this wonderful vlog (video blog) by blogger Chaviva Galatz, a fellow Orthodox
By the way, I'm not just bored by telling my story. I've come to realize that once I start talking about my relationship with G-d spurring me to convert, people stop listening because that's not what they expect. They expect to hear how I met my husband and he inspired me to convert. They don't expect to hear I was converting before I met him as a single person. They don't expect to hear about my passion for Judaism and for G-d...one I had as a non-Jew and now as a Jew.
Also, now that my status is kinda confusing.... Yes, I converted but I probably didn't have to because my family believes that my MATERNAL great-great-grandmother was a Turkish Jewish descendant of the Sephardic community in Akhisar, Turkey. Very few people, outside my close family, have been very excited about this news. Even my own friends find it too shocking to believe and didn't mind telling me so. Thanks, pals. Really. Yes, my formerly anti-Semitic family loves lying about being Jewish. Seriously?