#Groovy, 34 bytes

{it.sort{it.toLowerCase()-'the '}}

41% my answer is .toLowerCase(), kill me now.

#Output

When running...

({it.sort{it.toLowerCase()-'the '}})(['The ramones','The Cure','The Pixies','The Roots','The Animals','Enrique Iglesias'])

The result is...

[The Animals, The Cure, Enrique Iglesias, The Pixies, The ramones, The Roots]

With no debug or error output.

Groovy, 34 bytes

{it.sort{it.toLowerCase()-'the '}}

41% my answer is .toLowerCase(), kill me now.

Output

When running...

({it.sort{it.toLowerCase()-'the '}})(['The ramones','The Cure','The Pixies','The Roots','The Animals','Enrique Iglesias'])

The result is...

[The Animals, The Cure, Enrique Iglesias, The Pixies, The ramones, The Roots]

With no debug or error output.