My family supports Liverpool, so they're my team in the PL & they were the club that originally got me interested in football. So I know quite a few Liverpool fans, both from having been there & ones I've met elsewhere/the internet. There are some that fit the definition of delusional, but a lot are just optimistic, which isn't a bad trait at all. I suppose there's a fine line though.
Liverpool are historically a big club, there is no doubt that one day the club will win titles again. Football goes in cycles, you can already see it happening with Liverpool getting a lot of positive results, while United is becoming a midtable team. So for fans to be optimistic about the future is a good thing.
Where it gets annoying is when they start to feel entitled & become arrogant. Those people aren't necessarily the majority, but they are quite vocal. But like I said earlier, every club has these types of fans.