You need to create a corporate culture of accepting headphones.
This is tough to do, but there have been occasions in the past where it has happened. If you fail to do this, you will possibly be a social outcast, and this has implications for your life.
Studies by Smart People (1, 2) have shown that people with more friends live longer - people with more than 5 friends live on average ? year longer! By taking chances with being a social outcast, you risk reducing your friends. You are literally killing yourself in the future by taking a risk with headphones. MURDERER.
So, given we have a really bad scenario, the ways to alleviate it are:
pivot your company to accept headphones by creating a company strategy of selling them.
Successful companies in the past that have done this include:
Beats, by Dr Dre. Beats pivoted from literally selling nothing (another casualty of the GFC) to selling headphones in a nanosecond. The company culture was probably pretty accepting of headphones. They did this by hiring a famous rapper and then selling headphones.
Apple, by Turtleneck. Apple pivoted from selling cables, cases and etc to buying Beats, by Dr Dre, and then selling headphones. Nobody knows how they did this.
I would suggest then that you argue that your company buy Apple, by Turtleneck, and then sell Beats, by Dr Dre. Or, reduce your company sales to 0 and then pitch the idea to sell headphones by way of a famous rapper.
The benefit of all this is that you will probably have good stories, which one of the studies linked to suggests as a good way to make friends. The other study used a picture of babies near water to suggest life expectency, so maybe you can sell headphones and stories by the beach to babies?