Yes, .org is an open and unrestricted domain. Anyone is allowed to register and use .org domain names.
.org is the home for millions of nonprofit websites, including charitable, artistic, scientific, personal, educational, social, cultural and religious sites. .org sites are run by clubs, incorporated and unincorporated not-for-profit organizations, industry associations, families, individuals, schools, foundations, and more. Even for-profit companies have .org sites devoted to their charitable or volunteer programs.