But the negative connotation are only in the mind of people who want to stay away from those types of people. I think for the most part people who are those that are being labeled take pride in their name.
For instance someone who is secular may take pride in himself as a “secular person” for his “logical, scientific” approach to life as opposed to the “religious” Jews who are “illogical, cavemen”.
On the other hand a religious Jew will take pride in his being “religious” because he lives a life of emes as opposed to the “secular” who live lives of “taiva”.
(this was only an example of what people may think- please don’t read too deeply into it)
Charda”l: Chareidi Dati Le’umi. They are the type of people who send their children to hesder yeshivas. They may have long peyos and beard but dress in jeans and a t-shirt.