I have 2 road bikes. I am 67yo. I have modified the bikes a bit in that:

1. My bars are just a slight bit lower than the saddle, contrary to many folks whose bars are considerably below the saddle.

2. I have "in-line brakes" installed so that I may have excellent braking while using the bars as a riding position.

I also have a mtn bike, and my wife has a hybrid and a mtn bike.

Yes, lots and lots of "older" types around here ride road bikes, including a friend who is 75yo.

But, the very fact that you asked the question indicates that you are having some doubts about your bike.

Don't.

Each of us finds our own way which is best suited to our time in space, our budget, our goals and our personality. Hopefully, by the time one is 50+ he/she doesn't give a hoot about what others say or think.

Keep riding as you like. Besides, for the same mileage, you are going to burn more calories and get more exercise on a hybrid than on a roadie.

Keep pedalin'.