You have drawn an unjustified conclusion from your google search. Talmudic or Rabbinic Judaism is the term used in contrast to the Judaism that practiced Temple centered worship. Temple worship came to an end when the Romans burnt down the Temple at Jerusalem in the year 78.
There is no pejorative.
It might be a pejorative to a Karaite Jew
Since you know that the Temple burned 2000 years ago which ended the era of “Temple centered worship” why did you feel the need to call today’s Jews “Talmudic Jews?” And since your statement was quite hostile and derogatory towards your named “Talmudic Jews,” [”I maintain for all practical purposes there is NOTHING she could have said to keep from provoking Talmudic Jews without actually denying her faith”],and since by your own definition all post Temple Jews, ie for the last 2000 years, are “Talmudic Jews” I took that as a negative reference to Jews and their holy texts.
Today since the Temple is long gone Jews are just known as Jews, no adjective required.
But if you must use one the preferred terms are Orthodox, Conservative and Reformed. There is the rare Karaite as well.