Why do some people adopt an ethnicity that does not appear to be their own?

Because New Zealand has an official concept of ethnicity that is based on self-perception, Ms Dolezal (if she was a resident of NZ) would be free to nominate any ethnicity or ethnicities she felt she belonged to, and be enumerated as such.  In the Australian context, Ms Dolezal would be officially regarded as European, and not African-American or Negro for the purposes of past or present censuses, since the concept of ethnicity is not used in the Australian Census (including in the Indigenous question).

While official classification is one thing, social recognition is different and many people will not be swayed by official definitions, instead using their own standards. 

People have mixed views on whether to emphasise race or ethnicity. 

Ethnicity has the attraction of being the identity consented to by the individual concerned.  Its disadvantages are that it is not objective, relies entirely on self-assessment, and often cannot be determined without interrogating the individual. 

Race, on the other hand, is largely an objective concept (as are the concepts of "ancestry" and "origin"), and race can be easily used to informally categorise the background of others because physical characteristics (used to assess race) are visually discerned, even in the case of strangers.  Most people, however, recognise that some aspects of a race-based approach (e.g. past reference to half-caste, percentage blood, reference to skin colour etc) are "not nice", and can be insulting to persons of mixed racial descent.  Genetics can also produce outliers insofar as persons largely of a given racial descent can randomly end up with physical characteristics more consistent with their secondary ancestry.  In Australia, many of those of less than 50 per cent Indigenous descent (classified by their non-Indigenous race up to 1966) often not only “felt” Indigenous but had Indigenous identity imposed on them by the general community, if they displayed  identifiable Aboriginal features. 

There are lots of cases, where people seem to "adopt" a new racial, ethnic, or national identity.  A very interesting case is that of Seán Mac Stíofáin, sometimes called the "English Irishman".  He was someone that most people would have regarded as a most unlikely candidate for Chief-of-Staff of the Provisional IRA.   

He was actually born John Edward Drayton Stephenson in Leytonstone, London in 1928.  His parents (despite reports claiming that his mother was Irish-born) were English (she was born in Bethnal Green, London).  His only ancestral connection to Ireland was that one of his great-grandmothers was born in Protestant East Belfast.

Stephenson was baptised a Protestant, but was sent to Catholic schools in London as a child, and became Catholic.  After leaving school in 1944 and working in the building trade, he was conscripted into the RAF in 1945.  After leaving the RAF, he returned to London, where he became increasingly involved with nationalistic Irish organisations, learnt to speak Irish, and eventually joined an IRA unit. He met and married an Irishwoman.

In 1953, he took part in an IRA arms raid on the armoury of the Officer Training Corps at Felsted, a private school in Essex.  He was caught, convicted and spent six years in jail.  Upon being granted parole in 1959, he moved to the Republic of Ireland with his wife and young family.  He became known under the Irish version of his name, and continued his involvement with the IRA.

In 1969 the IRA split on the issue of the old leadership's increasing Marxism, and on the issue of defence of Catholic ghettos during Northern Ireland's early "troubles".  Mac Stíofáin became the inaugural Chief of Staff of the breakaway (and subsequently dominant) Provisional faction, when the "troubles" were at their peak.   Nicknamed "Mac the Knife", Mac Stíofáin was said to be a dedicated "physical force" republican, who developed the strategy of random car-bombings, and personally authorised the Bloody Friday bombings of July 1972 in Belfast (when nine people were killed and around 130 injured).  A leading rival IRA leader claimed that "he spends all his time going around trying to prove to everybody that he's as Irish as they are, and in the IRA he had to show that he was more violent than the rest".

Mac Stíofáin's downfall occurred in 1973 following his failure to complete a hunger and thirst strike, after being jailed for IRA membership in Dublin.  He was replaced by younger more politically aware activists.   Mac Stíofáin went into relative obscurity and died in 2001.

So why do people adopt an ethnicity that is inconsistent with their main heritage?