@Marian Lol I was saying this more for fun…didn’t really believe he would grab more towels, but good to know, thanks!
I lived in co-ed dorms and used co-ed bathrooms back in the 1980’s. So did my husband, at his (separate) college. From both my perspective as a woman and his perspective as a man, it was a perfectly comfortable experience. We are glad that our son’s college has co-ed dorms; certainly, he would never have wanted to go to a college that did not!
It is nice to have opportunities to interact naturally with members of both sexes through daily interactions. As a female non-drinker, I was much more comfortable getting to know guys through natural conversations in a dorm at random times of the day than at parties. Whether in your common room, in the hall, at the bathroom sinks, or at the laundry machines… you will be chatting about regular daily life, free from any pressure. You are not meeting people only when you are trying to. You are meeting people just because you see them every day.
You hold doors open for each other and talk about the weather. You help each other figure out the laundry machines. You may participate in shared readings and discussions and weekly snacks as a dorm unit. Just normal daily interactions!
Sometimes people imagine something like co-ed gang showers, but that is not the case! There are private stalls for showers and toilets. You have privacy. Your genitalia will not be on display! People wear robes or towels, usually robes, as they walk down the hall and when they are at the sinks.
But if you have religious reasons or strong personal comfort reasons for a single sex bathroom, let your college know. Colleges value diversity and will support you by setting you up in a comfortable living environment. No college wants you to feel unsafe or untrue to your beliefs. Absent personal religious requirements or PTSD, however, you probably will feel very comfortable in a co-ed dorm before long.
(I wrote this for any student or parent who might read it and be wondering about co-ed dorms and bathrooms. In your daughter’s case, since she is asking you if it is okay, it sounds like she is comfortable with the idea, and just needs to hear from you that you trust her judgment.)
When I lived in a coed dorm I walk down the hall in a bathrobe. It covered up a lot more than I wore the rest of the day.
I choose a single sex dorm for freshman year back before computers but after erasable typing paper. I wanted to look put together when I was around guys, and not like I had just gotten out of the shower. It was a personal decision, which I know some women still prefer. By sophomore year, I moved to a suite style coed, and liked that. DD1 lived in a coed dorm all four years…I brought my reasoning up to her as she was choosing,and later in the Spring asked her how it had gone. She said that she enjoyed the bathroom bonding with the other girls, and was glad they were separate. She said that people rarely date on their floor because it would be like dating your brother. She never had a coed bathroom: every floor had a women’s and a men ‘s unless there were suites. I would be more concerned that your daughter investigates the bathroom situation and makes sure she is comfortable with it. I think most schools have varying choices, but we did run into one school where all bathrooms were coed unless you were in a single sex dorm. I believe it was Vassar. There was one grandmother on the tour that I thought was going to pass out when the tour guide blithely mentioned it. DD2 was quite clear after the tour that she did not prefer coed bathrooms, but didn’t have a strong opinion on coed vs girls. I plan to remind her of this when she chooses her dorm, as my guess is that different dorms have different policies at her chosen school. I would never presume to make this decision for her… it is one of the many that she will make independently.
“I wanted to look put together when I was around guys, and not like I had just gotten out of the shower.”
This reminds me of The Marvelous Mrs. Maisel. 
My D’s suite sophomore year was 3 girls and a guy - the guy was her roommmate. No issues.
OP, not knowing your background, I’ll just assume you’re a concerned parent. To me, co-ed dorms are the norm. I lived in a suite style dorm (one gender in a suite) at a big state school for two years. Each floor had equal numbers of suites per gender. It was very unusual to have someone’s significant other stay over night. If they did, the guest was the one who was shy/on-best-behavior as they were in the minority, gender-wise. Sure, there were hookups etc infrequently (probably not often across the whole floor over a year) as most people were frosh/sophomores and weren’t dating often. In fact, the more “active” people usually fled to frats/sororities or apartments earlier than most.