The notion of male privilege is bigotry, and assumes moral superiority and higher virtue for women.
Maleness in and of itself does now bestow privilege upon a person. Privilege is a very complex manifestation of many circumstances and characteristics.
What we see now is that the word “privilege” is used as ad hominem attacks on the personal characteristics of people in order to other, dehumanise and diminish, and it is normally deployed by those with fragile intellects and egos who are upset when their worldview is challenged in any way.
With regard to the specific example of the OP, it is ok for someone to be scared when walking alone at night, but it is not ok to attribute this fear to the protected characteristics of other people. The fear felt is real and it matters, but it is a matter for the person experiencing the fear, and not the fault of an innocent person walking down a street minding his or her own business.
I know many women. None of them are scared to walk down a street at night and the perpetual trope of women as weak victims does not serve women, or anyone. It holds people back and perpetuates a mindset and culture of fear, for a demographic who should be becoming more empowered as violence against them from all demographics reduces statistically with ever passing year.
There has never been a better or safer time to be female, nor indeed to be human in the UK.
Statistically, males have more to fear from other males when out alone at night, and even that is reducing as overall crime rates continue to reduce.