The principle of the social services is that people have rights to live happily and without discrimination.
I know, I know. You mention more than one right. Normally your teacher would be yelling at you to add an ‘s’. But this is a vocabulary/collocation issue.
You can think of it as a phrasal verb (Indonesians will be translating berhak untuk..). Sometimes it’s have the right to + V1. Sometimes have a right to + V1.
Try googling “have the right to” and then “have rights to”. Which is more common? Which is the meaning that you want?