Amani Alkhat, the founder and editor of website muslimgirl.com, said Monday that despite the cultural change in Saudi Arabia spearheaded by Crown Prince Mohammed bin Salman, it has always been ultimately the woman's choice to cover herself in public and that that Saudi government just ended up interfering with everyday life.

"It's really important for us if we're discussing Saudi politics to really just keep it distinct from really attaching those policies of what we perceive to be as limitations to women ... it's really important for us not to attribute that to the religion or the culture itself," she said in an interview on CBSN. "I understand where the prince was coming from when he said that it's the women's choice to wear the head scarf -- inherently yes it absolutely is the choice of the women -- but unfortunately with many patriarchal governments like the one that Saudi Arabia is currently trying to evolve from right now, we see those things become policies that the government interferes in, where it shouldn't."

Crown Prince Mohammed bin Salman, 32, gave his first American network television interview on "60 Minutes" Sunday night ahead of meeting President Trump at the White House on Tuesday. The crown prince touted his country's progress for women's rights during the interview with CBS News' Norah O'Donnell and addressed women's choice to wear a head scarf in public -- something that used to be strictly enforced by so-called "religious police."

Amani Alkhat CBS News

In the wake of the interview, Alkhat explained her daily routine when she walks around in public.

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"Unfortunately men making comments about the way women dress seems like a universal tendency for guys ... whether it's conservative men telling me 'why is my neck showing from my head scarf' to men here in the states telling me to 'take my head scarf off' ... I don't think it necessarily represents the capabilities of what the government is headed towards."

Alkhat also addressed so-called "guardianship laws" even though women in Saudi Arabia are able to drive and attend sporting events.

"Guardianship laws basically stipulate that even though women are gaining these rights, it comes with an asterisk which is that they are only able to put them into practice if they have that 'legal guardian' or that male in their family or their household accompany them," she said. "Again, this is something the government has no business in and it's something I believe that should be completely separate between government and people's personal lives and how they practice their religion."

Alkhat is hoping that this "asterisk" is removed and that this is all one step in the right direction for women. "Let's reach that equality we're all yearning for," she said.

Known by his initials -- "M-B-S" -- Mohammaed bin Salman's reforms inside Saudi Arabia have been revolutionary, as documented in Sunday night's "60 Minutes" interview. He is emancipating women, introducing music and cinema and cracking down on corruption in a land with 15,000 princes.

Crown Prince Mohammed has curbed the powers of the country's so-called "religious police," who until recently, were able to arrest women for not covering their heads and bodies. In the interview, he was specific about what is Islamic law -- and what isn't.

"The laws are very clear and stipulated in the laws of Sharia: that women wear decent, respectful clothing, like men," Crown Prince Mohammed said. "This, however, does not particularly specify a black abaya or black head cover. The decision is entirely left for women to decide what type of decent and respectful attire she chooses to wear."

However, the CBS News team covering the story in Riyadh for a week, producers Graham Messick and Vanessa Fica witnessed first-hand the impact the crown prince's reforms are having -- and some of the growing pains of a changing society.

In an interview with "60 Minutes" Overtime's Ann Silvio, producer Fica explained that the broadcast team was outside on a sidewalk, waiting for a restaurant to open, when a car pulled up next to them. A man from the Saudi religious police began shouting in Arabic through a megaphone, imploring Fica to cover her hair. Fica replied that she didn't have a head covering, and after some negotiating, the man drove away.

"We were surprised, but we're pretty read-in here, and the religious police have lost their ability to make arrests," Messick explained.

"60 Minutes" associate producer Vanessa Fica was stopped by the Saudi "religious police" for not wearing a headscarf. After some negotiation, they drove away without incident. CBS "60 Minutes"

When O'Donnell relayed this story to Mohammed al Sheikh, one of the crown prince's closest advisers, he suggested that the incident shows how much the crown prince's reforms are impacting society. "See?" al Sheikh said. "About three years ago, you probably would have been arrested."

While in Riyadh, O'Donnell also left her hair uncovered, but she wore a long black abaya as a sign of respect. She said the crown prince sees issues like women's dress as a difference between religious and cultural influences.

"I think he's trying to teach people about Islam, and that's why he talked about bringing back to a more moderate Islam," O'Donnell said.

To see more of CBSN's interview with Amani Alkhat, watch the video at the top of this page or click here.