On Tisha B’Av it is assur to wear leather shoes. Crocs are synthetic and do not contain any leather. However there is a Machlokes between Rashi and the Rambam if wooden shoes that are not wrapped in leather, are assur on Yom Kippur because since you cannot feel the ground they are like shoes even though they don’t have leather. The Shulchan Aruch (614:2) paskens like the Rambam who says that it is permissible while the Mishna Brura (5) says we should be Machmir like Rashi.
On one hand, Tisha B’Av is not as stringent as Yom Kippur, which is Min HaTorah, so maybe we need not be machmir. On the other hand, Crocs are worn by millions of people as shoes every day of the year. The Gilyon Halacha U’Maaseh asked the leading poskim their opinion.
Rav Elyashiv said that since Crocs are worn all year round you are not permitted to wear them on Tisha B’Av. Rav Moshe Shternbuch said that while technically you may wear them, on Tisha B’Av it is better not to. Similarly Rav Nissim Karelitz and Rav Meir Brandsdorfer held that it is not assur but Yirei Shamayim should not wear them.