Assuming you're talking about the icons running down the left hand side of the screen you can try to unpin everything. I haven't tried it but, according to the manual, you can "unpin" all of your objects (ships, planets, etc) at once by pressing Ctrl-`. That's either an apostrophe or the little accent mark next to the "1" key, I'm not sure which.

It's probably not a toggle though so you'll have to pin everything back on your list. Just select the object and then click the little thumb tack looking icon in the upper right corner of the screen.

There's a checkbox in the interface menu that removes unit icons. Note that this will remove zoomed out bars around planets, and ships in phase space also. But it'll let you watch all the pretty pew pews

Have you tried ctrl+shift+z?

That was the problem. I still had my fleet selected so when I went into cinematic mode all the ship icons were still visible. Unselecting the fleet solved this.

Thanks for the help everyone.

I don't know for sure, since I'm new, but I believe pinned ships will only matter if you unpin the planets that the ships are orbiting. By default, all planets are pinned when you colonize them. If you select the planet on the tree and click the pin button, the planet will then dissappear from the tree unless it's selected in the main window. I think the same goes for ships, as well.

I'm going to try plying with only a handful of my planets pinned, and fleets only. It seems like it might streamline things a bit.