New players should not be bullied into skipping cutscenes, or locked out of battles!!
I concur with the earlier posters who point out that all too frequently veteran players seem to forget that they were once new to the content, or to understand that some players (often Final Fantasy fans, unsurprisingly enough) really appreciate experiencing the game narrative in context rather than watching it on YouTube or in the Inn.
Fortunately after one awful group I managed to get a party of helpful players (notably tanks and healers) for the Praetorium who said that they watched the cutscenes when they were new without being locked out of battles and encouraged me to do likewise.
Unfortunately if people are overgeared they can basically rush through everything and even ignore most mechanics. Instituting iLvl sync would help, at the possible expense of reducing the number of players in Duty Finder.
As suggested, Party Finder and making friends in the game is the best solution. Recently I was in a learning party of people on my server for Turn 1, and it was great!