Learn Italian: Le loro sorelle sono giovani.

The rule about dropping the article only applies to singular family members. When talking about plural family members (like sorelle instead of sorella), you always need the article. Additionally, loro is a special exception: it always keeps the article anyway, even with singular family members!

Why doesn't loro change to match the feminine plural noun sorelle?

Unlike other possessives that change endings to match the noun (mio, mia, miei, mie), the word loro (their) is invariable. It never changes its spelling! You just change the article before it (il, la, i, le) to match the noun's gender and number.

If sorelle is feminine plural, why does the adjective giovani end in -i instead of -e?

Adjectives that end in -e in the singular, like giovane (young), don't have separate masculine and feminine forms. They just change their ending to -i for all plurals. So, giovane becomes giovani whether you are talking about a group of brothers or a group of sisters.