Does the clear, white, mucous-like fluid that exits the vulva without lust, as a result of being affected by exciting speech, necessitate Ghusl?

The fluid in question does not necessitate ghusl (ritual bath). Ghusl is only required upon the emission of maniy (semen), and this fluid is not maniy. If it is emitted as a result of aroused desire, then it is madhiy (pre-seminal fluid). In this case, one must purify whatever it touches on the body and clothing, and perform ablution (wudu') for prayer. However, if it is emitted normally, not due to desire, then it is among the vaginal secretions (rutubat al-farj), which are considered pure according to the preponderant opinion, but they do invalidate ablution.