No one is entitled to forcing you to skip cutscenes during any dungeon. If they kick you for it, it's an abuse of the vote-kick feature and you should report them.

Conversely, no one is entitled to making the entire party wait for you to finish watching the cutscene before engaging the boss. Their time is just as valuable as yours and if you get locked out of the battle, don't make a stink about it.

If you REALLY want to watch the cutscenes AND participate in all the fights, make a Party Finder or ask your FC/LS to help you through it. Or, if you're a scumbag, queue in a party with yourself and either both healers or both tanks who are willing to wait for you. It will be mostly impossible for the rest of the party to charge through if either both tanks or both healers are waiting for you.