Is it safe to have sex with no condom on the pill?

That depends on how long you have been taking your pill. Here are the different scenarios and whether or not you’re protected if they apply to you:
1.) You just started taking birth control on a day that isn’t the first day of your period. You won’t be protected until after 7 days of continuous use.
2.) You start birth control on the first day of your period. You’re protected right away.
3.) You’ve missed one pill that wasn’t the first or last active pill. Take it immediately and then take the one you’re supposed to take today. You’re protected.
4.) You miss two or more pills. You need backup contraceptives for 7 days. Take the two pills you missed then take the one you need to take today.
Basically, if you’ve been taking your pills perfectly, there’s less than a 1% chance that you’ll get pregnant, even if your boyfriend ejaculates in you.