I’d assume [name]Clare[/name]/[name]Claire[/name] and [name]Carol/name were female, but [name]Clair[/name] and [name]Caroll[/name]/[name]Karel[/name]/[name]Karol[/name] I’d assume male.
[name]Clare[/name] is the English female form of the name, while [name]Clair[/name] is the more common masculine form (from the French. St [name]Clair[/name], [name]Sinclair[/name] are also well documented as given names in English). [name]Clair[/name] remained in the US top 1000 as a male name until the mid-1960s, and there’s no real reason why it couldn’t come back. I think it works on either gender, but I do prefer the [name]Clair[/name] spelling on a boy (much as I prefer [name]Francis[/name] on a man and [name]Frances[/name] on a woman, but nobody made that distinction in English until the 19th century).
[name]Carol[/name] I do think of as female in English, I think partly because of the word ‘carol’, and partly because [name]Carol[/name] has been used very intensely as a female name for a very long time. Sure, it became popular as a woman’s name in the 30s and 40s and 50s, but it was used as a female name before that (albeit a rare one).
The other factor here (and I think this might answer your larger question) is that [name]Carol[/name] was a top-50 name in the US for 40 years, during a time when most babies were given a top-50 name. When [name]Carol[/name] was #5 in 1945, more than 2% of baby girls born that year were called [name]Carol[/name]; in 1968 when [name]Carol[/name] was #49, almost half of a percent of girls were given that name. [name]Madison[/name] peaked at 1 percent in 2002; last year, although it was still a top-10 name, just over half of one percent of baby girls were called [name]Madison[/name]. So a much higher proportion of the female population has been named [name]Carol[/name] than will ever be named [name]Madison[/name], [name]Morgan[/name], or [name]Avery[/name], meaning that personal and cultural references for [name]Carol[/name] (and [name]Beverly[/name], [name]Shirley[/name], and [name]Leslie[/name]) will be more female than they are for some of the newer ‘crossover’ names. That said, [name]Caroll[/name] and [name]Carroll[/name] read male to me, and I wouldn’t be surprised to hear more male Carrolls 20 years from now.
[name]Shirley[/name] and [name]Beverly[/name] might be permanently girls’ name, but I think [name]Clair[/name], [name]Karel[/name], [name]Robin[/name], [name]Morgan[/name], [name]Cary[/name], [name]Aubrey[/name] and many others are entirely wearable on a man. [name]Douglas[/name], which was originally a woman’s name, I think is permanently a man’s name now (just to give an example from the other side!).
[name]Philip[/name]/[name]Phillip[/name]/[name]Philipp[/name], [name]Benet[/name]/[name]Bennet[/name]/[name]Benett[/name] ([name]Benedict[/name]), [name]Franci[/name]/es, [name]Christian[/name]/[name]Christen[/name], and [name]Julian[/name] (primarily female) were all unisex names in [name]Britain[/name] for centuries. What would you think of parents of girls with those names now?