Personally, I do feel like it's something you have to train your baby to do. I've heard of parents who say their baby won't do.... whatever.... and my first question is always, "Well, how long did you work on it for?"
It's tough! Shopping with a tired and cranky 14 month old can't be fun!!! You find yourself planning everything around those naps, and while you're out, and naptime is getting close, you start sweating and stressing, wondering if you're going to make it home on time! Soon it gets to where it's just not worth leaving the house..... and not too long after that, you're a complete basket case because the walls start closing in on you.....
My advice is to pick a day, when you know your favorite place isn't really busy. Whether it's the mall, or Walmart, or Target.... wherever.... wait until he's close to naptime, then go to the place, and have at it! Walk the store until he passes out. As he's cranky and screaming, just talk to him calmly and soothingly, in a low voice. BUT, don't give him your attention. Be purposefully engaged in "shopping." You might absentmindedly stroke his hair here and there, or whatever, but don't give him your attention. Eventually he'll give it up and pass out. The first time will be the hardest, but after that it gets easier, because he will start to learn that, "Mommy is shopping and I am okay."
And no, you aren't ignoring your baby's needs. You are ignoring your baby's temper tantrum and in doing that, you are teaching your baby that throwing a tantrum doesn't work. And actually, at 14 months, he's considered a toddler..... in case that helps you mentally deal with letting him scream it out.
AND, don't worry about what other people are going to think. Toddlers cry. Most people understand that and those that don't obviously don't have kids!
Oh, and my advice is based on my own experience with probably the most strong willed, spoiled rotten, feisty little bugger of a princess that happens to be my now three year old daughter!