I'm really sorry you had to go through that Nekoko.
As shameful as it is to admit, this has been an ongoing problem since... well, pretty much 2.0 launch. (My solution to this issue is to simply make all CS in those dungeons unskippable, for everyone.)

However, know that after CM and Prae you will not have to suffer those types of people in story dungeons since SE chose to put them before and after dungeon completion.

The only thing I can tell you is to not let them get to you any more than they have. If you should ever run into this issue again, report the idiots for harassment asap.
Know that they do NOT have the right to force you skip cutscenes or fights. And they certainly do NOT have the right to belittle you because you want to enjoy the storyline.
In this case, those people are entirely in the wrong and they should feel ashamed.

I've said it before and I'll say it again- Watching the CS at the in is a cop out. Furthermore, people who have no desire to let newbies experience the story in those two dungeons should not queue for them. If they are after tomes, there are far more efficient ways to go about getting them.

Regrettably, some members of the FFXIV are huge jerks. There is not much SE can do about their behavioral problems. SE did try to help newbies out by throwing incentives for the vets to come back- i.e. large tome bonus, gil, etc but all it did was backfire.
There are a number of ways to combat these types of players. You can report them for harassment, stand up to them, or if need be, leave the instance.
Another thing you can do- and this is more for your sanity than anyone elses, is get a couple of friends to go with you. When I ran CM and Prae, I had as many friends as I could gather come with. We weren't a full group but we were the majority. Likewise, whenever an FC mate or friend needed these dungeons, I would try to get the majority of the players to be with me. Even if all you can get is one person, it's better than nothing. Sometimes all it takes is one person to side with you to break the sheeple herd mentality in these dungeons.

Lastly, know that these idiots are not the majority of this playerbase. They are a very loud and very vocal minority. Since 2.0 launched there has been a push to have more tolerance and respect toward newbies, especially by people who were also forced to skip cs and fights.

-feeds nekoko cookies- If you were on my server, I would have gone in with you and you would have enjoyed the dungeons properly.