PITTSBURGH — The two sisters know what people call them. “Traitor,” complete strangers write online. “Queer,” whisper other high school students.

Jackie Evancho, a 16-year-old singer who rode success on NBC’s “America’s Got Talent” to international stardom, has become the target of intense criticism over her decision to perform the national anthem at Donald J. Trump’s presidential inauguration on Jan. 20. Juliet Evancho, 18, has always defended her little sister, but she is dealing with blowback of another kind. Juliet came out as transgender in 2015, and her family is suing the school district over her right to use women’s bathrooms.

As the girls curled up next to each other on a sofa in their family living room in a Pittsburgh suburb on a recent evening, the pressures on them — and their devotion to each other — came into sharp relief.

Juliet, who has tagged along to Jackie’s performances for years to cheer her on — including at the National Christmas Tree lighting ceremony with President Obama in 2010 — said she would not travel with the family to Washington to celebrate her sister’s singing at the Capitol. Juliet said that she had become careful about “literally” everything to avoid fueling more criticism. Next week, she said, she has “prior engagements.”