I am the GM of all Asian operations, with a HQ in China. I have been living in China for over 15 years. I do employ a staff, and I do employ interns. I am now looking at hiring engineering interns. I have one from Germany presently. Another female from France that will arrive in two weeks, and I am actively interviewing this week.
I would NOT hire you.
When I do business in Saudi Arabia, I remove my Christian cross. I do not drink beer, wine or anything else. I observe their laws, and respect their way of life. I am forbidden to go anywhere near their holy sites.
All my employees, staff and interns OBEY Chinese standard rules of behavior written and unwritten. This is codified in a strict internship handbook. When you work for someone you adopt their dress code. It is not the other way around. When I first started working (a long, long time ago), I had to keep my hair over my collar, off my ears, no facial hair, and wear a white shirt with a bow tie. When you work, you OBEY the rules.

What a office woman in China is supposed to look like.
When you move to China you adapt to the Chinese way of life. You sleep on rock-hard mattresses. You drink 53 degree white wine, and eat fish heads. You wear the uniforms that they provide for you, and if required you dance and sing the company songs at morning muster. When the boss tells you that you must work on the weekend, you work. When the boss tells you that you will attend the KTV and sing four songs, of which two is a duet. You will do so. You will do so with a smile on your face.

Chinese professional woman at work in the office.
If you came to work for me, interviewed without a headscarf, and then tried to get away with wearing it, I would FIRE you on the spot and revoke your visa. Absolutely NO female shall wear a headscarf while in our employment. It is a company policy, and I don't bend or break policy for any reason. Now, there is a reason for this rule...
In China, everyone is part of a community. We all play a role. We are all equal. We all dress similarly and act similarly. No one stands out, except for the boss or a weiguren. If you want to stand out...go ahead wear the head scarf. The same goes for extreme tattoos, ear piercings and nose piercings. Go ahead put a bone through your nose. Go ahead wear bright orange shoes and dye your hair pink. You will be set aside as a non-person. You would be HATED as someone who rejects the Chinese way of life. You will be shunned as a person who thinks that they are better than the Chinese people that they work with.
Yes, there are Muslims in China and they do also wear headscarves. They are also SHUNNED.
Maybe you can find someone who will hire you with your behavior limitations. I think it is very rude for you to IMPOSE your behaviors on an employer who is taking a risk at hiring you. When you come to China you WILL adapt to the Chinese way of life and culture. Not the other way around.
I suggest that you try to find work in nations that allow your behaviors. May I suggest Egypt, Saudi Arabia, Dubai, Syria, Afghanistan, or Pakistan. There you might be able to be more comfortable and blend in easier.
A refusal to adapt to another culture will cause you a great deal of trouble in China.

Chinese female professional worker.
I know that this is harsh, but that is the way it is. This is not a nice safe space university campus. When you to intern you will work and you will obey the rules of the workplace. You had best get that chip off your shoulder right now. It's not doing you any favors.
I would suggest that you adapt to where you live. If that location is not to your liking or comfort, then don't go there. There are many other places where you can go and intern. Might I suggest Pakistan. There you can wear your headscarf and fit in quite comfortably. Another place is Indonesia. Or perhaps Malaysia. These areas all have large segments of the female population wearing headscarves.