A. Two words for you and the glaring beachgoers: mutual tolerance. Those who are not inured to the varied sights and smells associated with the removal of dirty diapers (those who are childless or would like to forget that particular aspect of babycare) may, understandably, be miffed at becoming spectators of your soiled-bottom cleanup. After all, they've likely come to the beach expecting broad, endless vistas, and to smell the comforting fragrance of sand, surf, and suntan lotion.
Still, a baby has a right to have her diaper changed when she needs it, and if the beach blanket is the most convenient and sanitary place for this task, then it's practical to do it right there. (Personally, I preferred taking my baby to the car for diaper changes, so long as the parking lot wasn't too far away and the day wasn't too scorching. This avoided the gritty sand-in-diaper-cream problem and its attendant irritation of tender parts.)
But you do have to show fellow beachgoers some consideration and be discreet. You might use whatever sun-shielding device you have the baby under -- an umbrella, a canopy attached to the stroller or infant seat, the stroller or seat itself -- as a privacy screen, throwing a towel over one side to block public view.
If there's anyone still glaring at you, smile and say, "She's a very modest baby," which should be enough to make them look away in embarrassment. Then finish up as quickly and efficiently as you can.