In these cases, if I just react by "Ahhhh~~~~😅" as I fail to come up with anything to respond, what kind of impressions do I make on the person?
Just the kind of impression you think you're making: That you don't really know how to react to the information. That's okay, but then it's up to you to keep the conversation going by providing a new subject to talk about.
Is there any better way to react in these cases, without offending them? (At least I'm more inclined to believe it is rather rude to ask a question abruptly, such as "Why did you become a vegetarian?")
I don't know a lot about vegetarianism or veganism either, but when talking to such persons, my usual go-to to keep the conversation going is:
Well, I'm obviously not. But tell me more, what is your favorite recipe?
Basically, asking a question shows that you're interested in the other person, that you respect their choice (pick the right question for that!). If you're still confused with the difference between veganism and vegetarianism, a question asking for an explanation of the difference like:
Oh, I heard that before, but I also heard someone mention veganism. Is it the same or are there differences? What are they?
Will give the other person a chance to explain and talk about their 'interest' a little. Once you've had a nice little chat, and it seems the person is willing to explain some basic things, you might ask them 'Why did you decide to become vegetarian?'. Make sure it's clear that you're asking this out of curiosity and that the person on the other side of the line shouldn't expect a load of critique on their identity, and you'll be fine.
As for topics like LGBT+ and religion, those are a bit more sensitive to talk about than vegetarianism, at least for me. My preferred reply to that is:
Oh, I'll try to remember it, and be considerate of it. I must admit I have very little knowledge or experience on the subject, so please feel free to let me know if I say anything that is inappropriate. And if you don't mind, I'd like to ask you some questions? You don't have to answer them if they get too personal, but it will probably help me understand you/LGBT/Christianity better.
But most of the time, from my experience, once people disclose they are < insert something here >, it means they are willing to talk about it. Just remember to be nice, and respectful. Never critique another person's identity but feel free to ask questions in a respectful way to gain a better understanding. As pointed out in the comments, a good rule of thumb is 'If it wouldn't be a polite topic with someone who is not < something >, it probably wouldn't be polite to bring up with someone who is'.
One last thing, if you're uncomfortable discussing the things people are disclosing to you, it's okay to say that as well, and ask them to respect your boundaries and not push the topic on you! I've had to do that several times before when people wanted to discuss being LGBT+ with me, while I was raised a pretty strict Christian (homosexuality wasn't something to be talked about etc.).
Oh. I'm not really comfortable discussing this topic. Can we change the topic to something else? Perhaps later I might be more comfortable discussing this with you, but for now, I'd really like to talk about something else.
This shows that you're willing to have a respectful conversation, but it also implies that if people keep pushing the topic, the conversation might escalate to 'not so nice'. You can explicitly warn them of this, when they keep pushing the topic on you. Accompany it with a chance of topic (nice weather huh?). Hopefully, this will help, otherwise there isn't much choice left but to terminate the interaction for a while.