It's unfortunate that it's come down to this, but in this day and age, many people are practically glued to their cell phones. People are taking their phones everywhere! They're even taking them on dates. What's worse than that, is that they're using them, and not turning them on silent or vibrate while on their dates. It's one of the biggest ways a person can show disrespect to another person while dating. You're on a date with them, to get to know them and to see if there's any chemistry. You should be giving your undivided attention to the person you're out with. How do you expect to see if there's a spark or develop any type of romance, if you're staring at your phone, instead of gazing into your date's beautiful eyes, while talking with them!
Talking and texting on the phone is one of the most disrespectful things that a person can do while on a first date. This goes for men and women, when I say that you should put your phones away, and be respectful to one another. If you have a purse, put your phone inside of it. If you didn't bring a purse, turn your phone facedown on the table. Your phone should be on silent or vibrate during a date. There's no need to send anyone a message, receive any messages, or take calls during a date. The only exceptions are if you have kids with a babysitter, you're a doctor and you're on call, or you have someone close to you that's very ill. Otherwise, your cell phones should be put away during a date.
If the other person happens to be using their phone or sending a message and they say that it's important, the appropriate response would be to let it go, and not to let it bother you. There's no need to call the person out on having bad manners, because it won't get you anywhere on this date. It will merely cause drama to bring up the subject while on the date. If that kind of behavior continues, I would bring it up in another environment or in a casual conversation, keeping it light. However, it's very disrespectful to the other person, unless it's truly urgent. Therefore, if one of you does the right thing and shows respect to the other, by not using your phone on the date, the other person might pick up on your good manners, and reciprocate your polite actions.