Basically, you need to realise that they are just people doing their jobs.
Being a Jack of All Theatrical Trades (instead of being dedicated to a single role), I have had occasion to work outside of the theatre business, on concerts etc and have worked on a couple of tours. Some times there are some really big stars, and you know what I learnt? In general, they are either just like us, or they are arogant pigs which disgust me.
As an interesting side note - I find as far as stars go, males are a hell of a lot easier to deal with. IN GENERAL. There are some great women stars and some shocking men, but out of those I have met... males are much easier to deal with and down to earth, which makes dealing with them a lot better.
That said, I tend to not get starstruck.
And just a note, call me a cynical a$$, but the higher you put them on a pedestal, the further they will eventually fall. So instead of idolising them due to their public persona, just treat them as real people, and if they impress you, great, congratulations, and if they are little prissy divas, you will not be inclined to take their sh!te.