Is it obligatory to wash clothes if a tissue placed inside them becomes wet with prostatic fluid (madhy), even if the clothes themselves do not get wet? And how can one distinguish between vaginal discharge and prostatic fluid, especially if the discharge is light yellow or transparent tending towards whitish?

If you are certain that the discharge is madhiy (pre-seminal fluid), then you must perform istinja' (washing the private parts) from it and wash whatever it has touched of your body and clothes. Some scholars consider sprinkling sufficient. If you are unsure about the transfer of impurity from the tissue to the clothes, the default is that it has not transferred, and the clothes are not deemed impure unless you are certain. If you are unsure whether the discharge is madhiy or a pure vaginal discharge, you may choose between the two, and both nullify wudu' (ablution), so wudu' is required. As for yellowish discharge, it is impure, and during menstruation, it is considered menstrual blood. Its ruling and the time at which it is considered menstruation have been clarified in previous fatwas.