Here is actually what the 4th Lateran Council said:
A difference of dress distinguishes Jews or Saracens from Christians in some provinces, but in others a certain confusion has developed so that they are indistinguishable. Whence it sometimes happens that by mistake Christians join with Jewish or Saracen women, and Jews or Saracens with christian women. In order that the offence of such a damnable mixing may not spread further, under the excuse of a mistake of this kind, we decree that such persons of either sex, in every christian province and at all times, are to be distinguished in public from other people by the character of their dress -- seeing moreover that this was enjoined upon them by Moses himself, as we read. They shall not appear in public at all on the days of lamentation and on passion Sunday; because some of them on such days, as we have heard, do not blush to parade in very ornate dress and are not afraid to mock Christians who are presenting a memorial of the most sacred passion and are displaying signs of grief. What we most strictly forbid however, is that they dare in any way to break out in derision of the Redeemer. We order secular princes to restrain with condign punishment those who do so presume, lest they dare to blaspheme in any way him who was crucified for us, since we ought not to ignore insults against him who blotted out our wrongdoings.
It specified some variety of distinctive dress, but not specifically pointed caps...
I wonder what the condign (fitting) punishment was?