Do remember, the Barbies ads and the Dora-as-princess stuff on even the most benign of children's television stations are a pretty relentless drumbeat for a kid. He probably doesn't associate princesses with being female per se as much as with being exotic and special, the way I felt as a little girl about sequins and top hats and capes. He also probably associates everything that is different about his sister's clothes with the inevitable fact that she is grown up compared to him.
My suggestion is to give him an option when you chase him out of his sister's stuff -- put together a bin (ostensibly for both kids) of dress-up clothes that include sparkly things, silky things, gloves, hats, feather boas, sports hats and jerseys, all the best oddities of human apparel. You might even do some garage-sale shopping for it. Then toss it in the corner of his room, point it out casually, and let him have fun.
I agree he is not being overtly sexual in the way an adult trying on the opposite sex's underwear would be. A 3-year-old just isn't at that point. They are more likely to be into it for the association with someone they love, as adgal says, or for the difference between the interesting clothing and their own mundane stuff. On a lark, last year I bought a sample-sale Italian tuxedo jacket for my son. Darned if he didn't want to wear it out to breakfast the other day, it is a lovely piece of work in top-quality fine wool and with satin shawl lapels. He resonates to it as luxurious and different.
I guess the other thing to mention is that that even if he did like women's underclothes when he grew up (and I don't think your story indicates he will), well, you love him anyway and it is a minor oddity to have, as things go. If he knows you are on his side all the time, he will do better in life. His choice of undergarment will not matter a darn compared to the security of having had a loving, supportive mom.
So all in all, don't worry!
I agree with SM. I have an almost 3 year old, and his favorite color right now is pink. He also asks to carry a purse (and will tromp around the room in my high heels carrying a purse) and at Halloween took one look at a Princess costume and asked for it. He told me h wanted to be a Princess like Olivia (his best friend). His number one influence right now is me. He spends most of his time with me. He is emulating what I do. I would suspect your son is doing the same thing. It would be normal and healthy for him to look up to his big sister, and want to be like her.
I agree with SM. I would tell him it's not ok to take his sisters things without her permission, and other then that, leave it alone. This is not a big deal at all.
Hm, I doubt he was actually 'embarressed' at three as their concept of things like one shouldn't wear other people's personal things or intimate things wouldn't really be too much yet. He was probably reacting to your tone and knew instantly that you didn't like what he was doing.
Kids of that age play all kinds of things. Rarely would a child of 3 think anything sexual of another's underwear.
I'd not make a big deal about it all and look at more of a situation that he was in his sister's things. That he needs to stay out of her room and frankly, just shut her door when she is not there. It's a no no to go into her room.
Good luck