I've heard this concern from many knitters. They spend a lot of time knitting a stunning shawl and then don't wear it because of the fear of looking like an old lady.
Here's a few tips to avoid that:
Stop calling it a shawl, it's a scarf. Words are powerful. If the word shawl feels old fashioned to you, pick a different label, scarf, wrap, or whatever name doesn't feel archaic to you.
Think about how you are wearing it on your body. The Internet has 29,700,000 results when I search "how to wear a scarf".
You can tie it, wrap it, drape it, fold it, pin it. You can wear it at the back, the front or on the side.
Give some thought to the rest of your outfit. If you want styling ideas look at how items are shown in the knitting magazines.
That issue has 32 patterns and a lace caplet is the one the editor chose for the cover shot.
Toughen up the rest of your look. I wear my shawls with leather jackets, boyfriend jeans, pencil skirts and motto or high heeled boots.
Or just get over it. Ageism is rampant in our youth obsessed culture. We don't need to buy into it! Try checking out blogs like Advanced Style where you'll see brave, individualistic fashion choices being made. Check out this Instagram challenge on challenging the silly rules of what not to wear after 30. I think we knitters need to show off our amazing work and be proud that we have things to wear that aren't mainstream, boring and available in every mall around the world.