There two separate questions here. When did humans start wearing clothes some of the time, and when did they start wearing clothes all of the time.

Lice that live on clothing are distinct from head lice. Genetic studies at the University of Florida estimate that these two species began to diverge when humans began wearing clothes around 170,000 years ago.

As to when humans began wearing clothes all of the time, you have to keep in mind that it varies by society as well as the specific time and place. We have stricter expectations of what you might wear to the office than what you might wear to the beach.

President Johnson was known to skinnydip in the whitehouse pool. From the 1950s through the 1970s, ivy league schools took nude photos of all incoming students as part of posture studies, something that we see as scandalous today.

I don't know when it passed the 50% point.

You might also want to ask the anthropologists over in our sibling subreddit /r/AskAnthropology.