I strongly discourage the idea of friendship between a boy and a girl if they do not have any reasonable and dignified relationship. Try to ignore such offers as long as you can and if you see that there is no more scene of ignoring then do say 'No' in very clear and noble manner. Don't be harsh because sometimes boys make it the matter of their ego and they can even harm you. There can be a friendship between opposite genders if there is dignified relationship exists between them like if they have a marriage bond, or they are siblings etc. I think a wife can have a friendship with his husband but a girl can not have with a boy.
This is separate issue to discuss the friendship between husband and wife because there are certain concepts regarding that like they can not be friends etc. So, do not give even a single thought to the idea of friendship with a man if you do not have any dignified relation with him. The other scene of the situation is that when a boy offers a girl to have friendship then she can not think anything good or bad as she has been overwhelmed by the feelings and might start friendship; a pure and sweet friendship?
Well nature speaks in this question that boys want to meet girls and girls want to see boys. Opposite attracts. Boys and girls have an attraction built in for each other as a basic feel or passion.
Getting an offer from a boy is just like a door bell call to open the doors, which in opinion should be opened. But this is also important that you should decide carefully to judge that person at the door, whether to let him in or just ask him to leave.
This way you are not only opening doors for him only you are also welcoming pleasure and happiness in your life too. You get the experience of your life with that interaction.
But again I will emphasize strongly on judging the persons. Take your time and assess that person, you have all the time in the world to accept or reject any offer like that. Even not accepting him as your friend would not be the end of the world. Along with this I would recommend not to develop your image as a closed person or rude. Just be bold and wise enough to decide in the proper time of frame. Be lively, you wont be short of such offers.
When boys offer friendship, I think friendship develops and if you get along with each other, there is nothing to be worried about. If someone has feelings for you, give him a chance. You should never refuse friendship since you never know when you will need a friend to talk to or in bad times.
As boys and girls get young, they start feeling attraction with opposite sex and for this purpose they perform many things full of wisdom or full of foolishness. Friendship between boys and girls is a natural phenomenon because attraction towards opposite sex is natural thing. Now we come towards your question that what you think girls should do when boys offer them friendship, I can give following suggestions in this regard.
When there will be many young girls, it is a natural thing that many boys with different characters and thoughts will offer them friendship according to liking and disliking. It is not compulsory that girls accept friendships from all the boys who offer them for the same. Girls should be sensible enough to choose the best boy among them for friendship and later on for marriage because it is an ultimate goal for every girl. In my opinion the girls of present age are quite sensible and they are always in try to choose the best boy with which they could make friendship first and later marriage.