No, i do not think it is safe to wear contacts with a popped blood vessel. Your eyes have the popped blood vessel maybe because your eyes have been infected by inflammation, so that it is so dangerous to wear contact at that time, even make your eyes' situation worse. You need keep your eyes to have a good rest and use some eye drops according to the doctor's advice. And after recovery, you can wear them again.
You'd better stop wearing the contact lenses these days to let the eyes have a good rest. The appearing popped blood vessel in your eyes means that your eyes are too dry. Working in front of computers for a long time with no rest may cause the eyes with contact lenses dry which indirectly cause the bloodshot. The early symptom of bloodshot is the popped blood vessel. If you keep on wearing the contact lenses, you may make it bad. Thus, let the eyes have the rest.
No, you should not wear contacts when you have a popped blood vessel in your eyes. When you have a popped blood vessel in your eyes, it may be because you are so tired or have some infection in your eyes. So in this situation, the first thing you should do is to have a good rest. And you can check your eyes and make sure they are fine. Then if they are still having a popped blood vessel, I suggest you can go and see a doctor. At this time, the popped blood vessel can be the symptom of an eye disease. So you should pay more attention to them.