I'm looking for a word which describes people who are annoying because they do something new, they think that this is so cool but actually the new thing and they are silly at all. The people I want to name think that they are romantics (romantics that Dostoyevski mentioned in Notes from Underground), but they are not, so I want a strong word that expresses the level of negative connotation I want.
Trendster, scenester, fashionista, faddist, dandy, gay blade, Beau Brummel, swell, fop, etc. In approximate coinage order of newer to older.
With the exception of "faddist", the problem is that during the spring of such words when new and freshly minted, these shiny words tend to be heard in a complimentary sense -- only as they age do they become pejorative, and at which point the words become as quaint as the fashions they derided.
Right now, 'hipster' might be a decent choice, but this most often refers to people of a particular style. I'd say that the negative connotation is often expressed in mood rather than diction. Accepting that, you could use 'avant-guard' or 'experimental' in the right context, especially with adjectives like 'oddly','absurdly, or 'quirkily'.
Perhaps, the word quixotic can help here.
: hopeful or romantic in a way that is not practical
They had quixotic dreams about the future.
in this age of giant chain stores, any attempt at operating an independent bookstore must be regarded as quixotic
Perhaps you find such people annoying because you consider them full of themselves.
full of oneself: (idiomatic) egotistical, believing oneself to be superior to others; preoccupied with one's own work, interests, point of view, etc.
"They do something new, they think that this is so cool but actually the new thing and they are silly at all." They are full of themselves. They don't see themselves as you see them.
Full of oneself is certainly pejorative.