Why did Caesar's Legion become hostile to me?

Did you perhaps have Boone travelling with you? If Boone is your current active companion, the Legion will always be hostile to you, because Boone will shoot them on sight, and they tend to return the favor.

Fallout New Vegas contains quite a few bugs like this. Because it's such a big game they are easily introduced and the steps to trigger them are usually quite opaque.

That said, the Legion does become hostile if you help the NCR so that might be the reason. Your status is set to neutral once when you receive the mark of ceasar, but when you continue to help the NCR (e.g. do a quest for them) it reverts back to the old (hostile) state.

If Boone is your companion the legion also becomes hostile, even if you set him to wait somewhere. You have to send him to Novac or the Lucky 38 through dialog to prevent that.

On PC: Make sure you have the latest patch installed. You can also install the "Community Bugfix Compilation Patch" which fixes a lot of known unfixed bugs.

Be careful about what clothes you are wearing. If you have on a rival tribe's outfit you will usually get attacked regardless of your reputation with that group.