Thank you for the thought-provoking questions! I probably spent way more time on this than I should have. 
[name_f]Do[/name_f] you think that a name has a gender?
I think that most names are typically associated with one gender or another in the US, and other English-speaking countries. [name_m]Even[/name_m] if it wasn’t always so, names become a “boy” or “girl” name depending on what is most common in society. The names themselves do not inherently have a gender, it’s just in people’s minds.
Should a name only be used on a certain gender?
I think it would be nice to have a society in which all names are gender neutral, but that just isn’t where we are right now. The way things stand, a boy named [name_f]Elizabeth[/name_f] is going to be teased, and people he meets are going to be confused. I also think that using traditionally male names on girls can create the same confusion, even though it’s much more common. So yes, I do think that names that are strongly associated with a particular gender should be used only for that gender.
What do you consider a gender neutral name?
Most nature names, like [name_u]River[/name_u]. However, there are natural objects that are considered more “masculine” or “feminine.” A boy named [name_f]Azalea[/name_f] is going to have the same troubles as a boy named [name_f]Elizabeth[/name_f].
When do you consider a name gender neutral? After it’s been used on each gender equally?
I feel like there can’t really be a set rule for this, because things change over time, or suddenly rocket into popularity, like [name_u]Madison[/name_u], [name_u]Morgan[/name_u], [name_u]Ashley[/name_u], [name_u]Taylor[/name_u], etc. However, if things are about even between the two genders, like [name_u]Taylor[/name_u] and [name_u]Jordan[/name_u] are for people my age, I would say yes, that name is (currently) gender neutral.
If a name like [name_u]Emmett[/name_u], the masculine form of [name_f]Emma[/name_f], can be used on a girl can [name_f]Elisabeth[/name_f] be used on a boy?
Any name can be used on anyone, but I don’t think it’s a good idea in our current society, for either a masculine name on a girl or a feminine name on a boy.
If it is okay to use traditionally masculine names on a girl, why isn’t it acceptable to use traditionally girls names on a boy?
Because being male is the default in our society, therefore masculine things are normal for everyone (or should I say “all mankind”?). A girl can go fishing, wear jeans, and build a fort. A boy cannot play with Barbies or paint his toenails. Girls are inferior, so why would a male want to do something that’s “for girls?” On the other hand, it’s natural for a girl to want to be more like the superior male. People pick up on this from a very, very young age and know that while girl things, including names, are not okay for boys, boys things are okay, or even good, for girls.
What makes a name more feminine or more masculine? Is it the sound of the name or the way the name looks when written out?
This also changes over time. Names like [name_u]Ashley[/name_u] or [name_u]Stacy[/name_u] (or your example, [name_u]Bailey[/name_u]) used to be fine for boys, but now the -ey, -ie, etc endings are assumed to be girls’ by default, or gender-neutral at best, with some notable exceptions like [name_u]Bradley[/name_u] and [name_m]Jeffrey[/name_m] (although judging from the numbers those two are definitely past their prime, at least for now, and most people go by [name_m]Brad[/name_m] or [name_m]Jeff[/name_m] anyway). Names ending in -a are also typically feminine, and even ones that aren’t may be assumed to be feminine by some people (ex your examples of [name_u]Asa[/name_u] of [name_m]Isaiah[/name_m]). I think tradition, popularity, and sometimes meaning make a name masculine or feminine, not the sound.
You always see celebrities and other people using traditionally masculine names on girls but never do you see it the other way around. A little while ago I met a little girl named [name_m]Isaiah[/name_m]. Her mother had said that she wanted to name her daughter something with the NN [name_u]Izzy[/name_u] and thought [name_m]Isaiah[/name_m] was perfect. When I told her that was my son’s name she asked me why I picked such a feminine name for my son.
She’s probably just making assumptions based on the “-ah” ending; lots of people don’t know much about names’ histories and assume that the way things are now is how it’s always been. Our society is obsessed with delineating between girls and boys, and many people are very uncomfortable with ambiguity in gender (that’s why you must have a blue or pink outfit for your baby at all times, so that strangers know whether to say “he” or “she” when discussing your offspring). I think that because girls are encroaching on traditionally masculine names, there’s a backlash of people feeling like they have to choose a super masculine name for a boy, so you can be super sure that yes, he is a boy. This just leads to even more names seeming to be more feminine and getting “lost” to girls.
If you met a little boy named [name_u]Bailey[/name_u] [name_u]Madison[/name_u] what would you think of him or his parents?
I might think that the parents were not up on name trends, or that they didn’t care that these names are now predominantly seen on girls, but since these are both traditionally masculine names, there’s nothing wrong with this name in itself. However I suspect that many people would be laughing behind their hands, or openly as the case may be.
Does that make [name_u]Bailey[/name_u] seem less masculine? [name_f]Do[/name_f] you think he would be a mama’s boy? Does it make you think less of him? Why?
I don’t think that the child’s personality would be influenced by his name, although I do think that parents may choose names that reflect their values, and therefore also how they will raise their children. Ex parents who name their child [name_m]Gunner[/name_m] might encourage (or tolerate) more aggressive behavior than the average parent; parents with a daughter named [name_f]Faith[/name_f] may be more religious and encourage it in their child. Parents who name their child a very feminine or very masculine name might encourage associated traits in their child. Obviously this wouldn’t hold true every time and would be a terrible way to make predictions about someone’s personality and behavior. And I wouldn’t think less of anyone for their name, since they didn’t choose it themselves.
A friend of mine I think said it best. Why is it okay for a family to decide to name their daughter [name_u]Asa[/name_u], a masculine biblical name but if you ask that same family to name their daughter [name_f]Abigail[/name_f] a feminine biblical name they wouldn’t even consider it?
I think sometimes choosing a traditionally male name for a girl is a question of people trying to find a unique but still recognizable name, or on the other hand, of following the trend of boys’ names for girls. In large part because of the internet, there’s such a fine line between cool and too trendy, and between too common and too weird, that I think people have trouble trying to navigate it and find a “perfect” name.