You can cry whilst wearing contacts like Cosplay Contact lenses.
You can still cry when you have your contact lenses in.
However if you do cry with your contact lenses in the tears may cause the contact lenses to not adhere to the inside of the eyes like they should.
So the contact lenses might fall out if you cry too much with them in.
If you know you're about to cry then it would be better to remove the contact lenses first but there are times where we cry without having the thought about taking the contact lenses out first.
I've cried before with contact lenses in and never had any issues but if you constantly cry with the contact lenses in the eyes may become irritated as well.