あいさつしないひとと対戦する必要あるんですか？
it's up to you. unless you'r in a tournament, you don't 'need to' play against anyone.
my understanding of etiquette is that it's good to greet the other player and wish them well
though from my personal experience, that's not always what happens
Lishogi has a "Kid mode" meant for children that disables all chats and personal messages, they could be using that. It's also possible that your opponents could have chat disabled to prevent harassment. Or maybe they just aren't familiar with the website, or aren't familiar with the etiquette of playing shogi. There's a lot of reasons they might not greet you.
Of course you don't HAVE to play against opponents who don't greet you; you could resign or abandon the game. But I think it's better to give the benefit of the doubt and just play on in any case.
Personally I always greet my opponent, unless we've already played many many games in a row and it doesn't feel necessary.
When I'm playing on the phone, greeting feels too obnoxious. It isn't mandatory, in any case.
You can't post in the forums yet. Play some games!