I really do think there is a component of reciprocity started by the RT OP. They post and basically ask 'the world' to contact them if they meet X criteria. As long as I reasonably do meet those criteria, I do as they ask. It's that simple. You asked me to contact you. You put time and effort into asking me to contact you. I didn't use a random phone number generator to text a stranger totally out of the blue. So, yes. I fulfilled step 1 of their request. I do feel they owe me 5 seconds to say "Sorry, not a good fit".
Now, for why it's rude. We're at a party together, therefore, we do have something in common, even if it's just knowing the host. I approach politely and try to make conversation. You turn to the side and flat out ignore me. Unless I did something rude first, you're rude. If you don't want people to talk to you, don't go to the party.
There's no way that not answering a decent RT reply isn't rude if it was translated into any face-to-face interaction. I hold myself an others to about the same social standards online as in person. Some rando hits me up on Facebook because I commented on a Buzzfeed article, no. I'm not obligated to reply. I listed my apartment on Facebook last December, and I didn't feel like showing the place to every person who responded. If they seemed super annoying, I did the courtesy of letting them know that I wasn't interested, as I absolutely did ask people to contact me about that. I have manners. I showed them, whether or not I wanted a Thousand-Question Karen in my home.
As for excuses, an anxiety disorder is about the only reason I'll somewhat accept. However, I was diagnosed with a severe anxiety and depression, and even before being medicated, I still managed to say "Thanks for contacting me, but I think we're not a good fit". Even if they're worse, I gotta wonder why someone who is struggling so much mentally that they can't do that minimum is out here inviting strangers to contact them... I don't feel guilty when I can't answer the phone because of a Flight reaction, but 90% of the time, I didn't ask them to call me, and I call those I did back when I'm able.
I just don't buy that one shouldn't maintain basic manners while online nor most excuses about why they don't.