Can "pigtail" be insulting in certain context?

Solution 1:

A pigtail is not insulting in current BE. It is not used as a racial epithet. It is simply a valid description of a hairstyle. In the 18th and 19th centuries British soldiers and sailors used to wear their hair in a pigtail.

Prior to the early 20th century, in the morals of the day, it was simply casual speech - an informal reference to a group of people - any insult would come from the context, rather than the word itself:

2b. colloquial (frequently derogatory and offensive). A person who wears a pigtail, esp. a Chinese person. Now rare or historical.

1886 Cornhill Mag. July 55 Sweetmeats..being great favourites with the ‘pigtails’.

The OED gives some of the history:

2.a. A plait or tail of hair. In early use: a single plait or queue of hair hanging down from the back of the head, as in a particular style of wig, or as worn by soldiers and sailors in the late 18th and early 19th centuries; a long plait of hair as formerly worn by the Chinese. Now chiefly: each of two tails of (usually plaited) hair hanging from either side of the head, as worn esp. by young girls.

1991 Hair's How No. 34. 808/2 Divide the ponytail in two, then plait to form two pigtails.

(A ponytail differs in that it is not plaited.)