Someone who converted is your "countryman." Love this person as you would love yourself and your loved ones, meaning, don't ask them invasive and personal questions that will make them feel alienated, exposed, and different. Welcome them with warmth and help them feel like they belong, just as you would want someone to help you feel like you belong. That is what"V'ahavta l'rei'acha kamocha" is all about.
When you ask someone about their Jewish legitimacy, you are humiliating them. Imagine someone who moved to New York City 10 years ago, and having someone say to them "You're from New York? I don't know about that -- you don't seem like a New Yorker. Where exactly did you grow up? What high school did you go to?" This feeling of making someone feel insecure and defensive, the Gemara describes this pain to be so harmful, it is as if you had spilled their blood.
The Gemara says that we will all descend into Gehenna at the end of our lives, but we will eventually become purified and ascend out of it and go to olam haba. However, there are a few folks who won't ascend. These are folks who have humiliated someone in public and those who have called someone a derogatory name. This would include telling someone "You aren't a real Jew because you converted Reform." That is humiliating. You're telling them: "You're a goy" or "You're a shiksa" -- which are "derogatory names."
If you humiliate someone in public, you will not be deserving of going to olam haba. Unrelated to conversion, but still worth noting: humiliating someone for committing a sin is even more serious than the sin itself. Your invasive questions can make someone feel really uncomfortable.
Tamar took the law of not humiliating someone so seriously, she was willing to be burned alive, rather than save herself by exposing her pregnancy which would humiliate Judah. (This story is very problematic.)
Verbally mistreating someone who converted (asking them personal questions and inquiring about their legitimacy) violates three laws, and oppressing them violates two laws. Unless you are that person's Cantor or Rabbi, it is not your job (and none of your business) to tell them about the difficulties of being married and having children in Israel. It can feel very oppressive.
מאי שנא מאנה דכתיבי שלשה לאוין (שמות כב, כ) וגר לא תונה (ויקרא יט, לג) וכי יגור אתך גר בארצכם לא תונו אותו (ויקרא כה, יז) ולא תונו איש את עמיתו וגר בכלל עמיתו הוא לוחצו נמי שלשה כתיבי (שמות כב, כ) ולא תלחצנו (שמות כג, ט) וגר לא תלחץ (שמות כב, כד) ולא תהיה לו כנושה וגר בכלל הוא אלא אחד זה ואחד זה בשלשה
This section highlights many passages in Torah that command us to treat those who have converted with respect. It refers to someone who has converted to be a colleague. You would not go to a colleague and act as if you are a "creditor," interrogating them and demanding answers.
If you cause a Jew-by-choice to feel uncomfortable and stressed about being in Jewish spaces, you will cause them to leave. They may very well return to their previous religion, which would be such a shonde! One thing the world doesn't need less of is another Jew.
This section really speaks for itself. Empathy! Relating to someone! We were strangers in the land of Egypt. We were nervous, afraid, and in need of kindness and understanding. So when you ask inappropriate questions -- questioning a Jew's belonging in a Jewish space -- you demean them and forget your own journey in Mitsrayim.