contribute

*The policy of multiculturalism has certainly contributed to establish the idea of equal rights and equal opportunity despite of the ethnic background.

Establishing. To is a preposition here, and establishing is a gerund, that is, a verb form functioning as a noun. Contribute is not followed by the infinitive.

Despite and in spite of are often confused, especially since they can be used interchangeably.

Despite the ethnic background of any citizen, despite your/one's/a person's ethnic background, or despite ethnic background. The here makes the reader ask, Whose ethnic background? It sounds unfinished.