The overriding answer as to why both of them cannot recognize their folly is because they did not see their love as one. In trying to find some meaning in their lives, seeking to defy the belief that their parents determine their autonomy, and finding a type of kindred spirit in the gaze of the other, neither one sees anything wrong with their love or infatuation. In the final analysis, it is this which allows both of them to plunge entirely into the other, losing sight of all else. They could not perceive themselves as foolish for they saw the world which could not understand nor appreciate them as foolish.
Romeo and Juliet were head or heels in love with each other. Love blinded them so all they all they cared about was being together. When two people fall in love, they become blind to foolishness.
They were also very young, although people did marry much younger during the time that this was written. They were both young teenagers and did not have a lot of life experience yet. The older a person is, the more experience they have.
They also came from two different sides of the tracks. They each had qualities that the other liked and because of this there was a great deal of attraction.
Good question. Young love says it all.
Romeo's words at the Capulet's party and his immediate move to kiss Juliet demonstrate he was taken with Juliet's looks, which most relationships start with anyway. And they should that is an integral part to a relationship that lasts: attraction.
Juliet does say
I have no joy of this contract tonight. It is too rash, too unadvised, too sudden;
She demonstrated here that she understood the foolishness of their relationship, however, she follows through later on all of her feelings. They both operate with their emotion as opposed to their knowledge.
Romeo's character is given to acting on his emotion as we saw him so depressed about Rosaline in the early part of Act I.
I believe these aspects of youth, acting on emotion instead of knowledge, and their inexperience with relationships led them to act foolishly, but almost unknowingly. This is a great story to demonstrate to parents that there are some issues that need to be discussed with their teens.
In my opinion, they do not realize it for three reasons. First, they are human and people are very much capable of making stupid mistakes. Second, they are people who are head over heels in love. When you are first in love, before your feelings have time to settle, you are more or less out of your mind and liable to do stupid things. Finally, they are young. She is 14 and he is not much older.
So when you combine these things, it is not at all surprising that they do stupid things. It's just too bad that their stupid actions get them killed.
In the play "Romeo and Juliet" the two are very innocent people. They have just begun their lives and they are not yet stained by the ignorant problems that their families have formulated. They are also in love with a deep and lustful passion that makes them blind to anything but their own desperate need to be together. Their innocence makes them trusting pawns in their own game at trying to sneak past their family members so that they can spend their lives together. Maturity would have wised them up some, but the adolescent love and childhood innocence did not allow them to see the full reality of their actions.