Is there anything stating women cannot wear their dress uniform instead of a bridal gown?

There's no reason she can't. Mountain out of a nonexistent mole hill...

Did the FB post say anything else? Did she actually ask about whether it was authorized or not? I would read her question to mean not that she couldn't wear it by regulation, but more that she was feeling social pressure not to because a lot of wedding traditions revolve around the choosing and wearing of the wedding dress. Like the one about the groom is not supposed to see the bride in her dress prior to the wedding.

Do not, let me say this again, DO NOT contradict a bride on her wedding even less on what she wants to wear!

Interesting question - would this be a male/female wedding or a female/female wedding? In a female/female wedding, where both were military, one wore a gown and the other wore their uniform.
Here is what a wedding site states:
Remember, wedding requirements vary depending on rank and military branch, so check with your base protocol officer to find out exactly what you need to do.
Wedding Attire - Probably the main distinction of a military wedding is that the bride and/or groom, as well as service members in the wedding party, usually wear their uniforms.
But, here is another source which should be the initial go to for this question - MilitaryOneSource.mil
And here is their initial statement - If you're getting married soon, congratulations! Planning a wedding can be a lot of fun — and a lot of work. If you're thinking about a military wedding, you may be pleased to find that there is no official protocol for military weddings. Instead, you can incorporate as many or as few military traditions into your wedding as you choose.

This is laughable. It may be rather unusual, but there is nothing prohibiting it beyond social norms.

I think you are right to Raise the BS Flag on this one! If I could wear my Dress Blues at my Wedding I can see no damn good reason that a Female Service member can't if they desire too!

Of COURSE they can wear dress uniform!

BS flag! If the groom could wear dress blues, then the bride could also. Equal treatment. Could make interesting wedding pictures.

No a service member may wear their dress uniform at a social event including if they wish. Not at political partican events however.

Although this question relates to a specific situation, I've noted other questions about active duty personnel regarding wearing their uniform to social events, on leave, and other circumstances. I'm always left confused.
Granted, some might consider the time I was on active duty akin to Washington crossing the Delaware, but the only active duty people I remember being required to have civilian clothing were those on Embassy Duty, or others who were going to be in foreign countries where there were not provisions for wearing of the US uniforms.
In the states, each of our uniforms was designated as being comparable to a specific civilian social attire, i.e. black tie, white tie, suit, business casual etc. While there were certain organizational or work uniforms we were not allowed to wear off base, there were none of our regular uniforms we were prohibited from wearing to any occasion other than a political event or an occasion that could potentially be embarrassing to the Corps. I even remember being told that our Alphas if we didn't possess Blues were appropriate at any civilian function.
Has our uniforms somehow become restricted?