Is it socially acceptable for individuals to wear clothing typically associated with the opposite gender? What are some reasons for or against this practice?

There are many reasons. This can be broken down into the eight broad categories below, though most people only think of no.6:

Reasons against it? Basically,

In Lancaster County, Pennsylvania or Salt Lake City it won’t be accepted. In Rio or Douarnenez at Mardi Gras it’s practically compulsory. (Seriously, I counted the men in skirts in a bar in Douarnenez: one in six.)

Flying Now Puts You At Risk Of Measles Exposure, CDC Says - Jalopnik

Ignore people who will quote their religion at you (unless it’s your religion too).

a) In serious entertainment, actors playing a role. From Mark Rylance as Cleopatra or Judi Dench as Olivia to Antony Perkins in Psycho. Japanese Kabuki and Nō players. Sopranos singing "breeches" roles in opera.

If it’s merely your sexual fetish — see 3) above — don’t do it in public. You’ll look ridiculous and possible offend decency laws.

Tom Hanks finally breaks his silence on daughter’s bombshell memoir: ‘Not surprised’ - New York Post

3) Fetish crossdressers - who use clothes as a substitute for, or an essential precursor to, sex. This is commonest among teenage boys, but usually disappears or develops into transvestism later. It is rarely seen in public, although the word "fetish" is often misapplied by those who should know better.

Socially acceptable? It depends on which bit of society you live in.

1) Occasional crossdressers - Hallowe'en, practical jokers, fancy dress parties, students' rags... etc.

Atque sapiente quis aspernatur.

b) In light entertainment: female impersonators/comedians; pantomime dames in British theatre.

Don’t do it unless you want to.

c) Drag queens and Drag kings – an exaggerated satirical sub-section of the light entertainment field.

What is the sluttiest thing your wife has ever done?

5) Other professionals: the occasional spy/undercover policeman/criminal in disguise. Gay prostitutes.

Don’t do it in places where it’s illegal, like Russia.

7) Transsexuals – for many of them the cross-dressing is merely an incidental stage in their transition of identity. Once achieved, the wearing of the clothes of the other sex becomes the norm, and can no longer be called crossdressing.

Fans slam Gearbox CEO Randy Pitchford's message to "cost sensitive" fans - Eurogamer

4) Entertainers.

6) Transvestites – what most people first think of. For transvestites, crossdressing is an end in itself; motives many and various. For most, these go back to childhood or before birth and are obsessive.

If you’re going to do it, do it 100% and do it well. You’ll enjoy it all the more and so will the people around you. It’s often good for a round of applause or a free drink.

Can it be true that people know your name, not your story, they’ve heard what you’ve done, but not what you’ve been through, so take their opinions of you with a grain of salt?

2) Fashion crossdressers - some metrosexuals and most women fall into this category. Women in trousers – seen as a sexual and social aberration in 1900 – had become the norm by 2000.

8) Those forced into crossdressing. This category is included for completeness but barely seems to exist in real life today. It was however observed in the period 1850-1950 when boys were occasionally forced into girls' clothes as a punishment at school or in the home. It is a staple of fiction – to escape from danger (Some Like It Hot), to obtain a job (Tootsie, Mrs Doubtfire), or forced by a sadistic female relative (much transvestite erotic fiction).

d) Stunt doubles.

They Just Wanted to Make a Space Movie. Instead, They Uncovered a Mind-Blowing Cosmic Secret - The Daily Galaxy