You are correct that "someone" is a singular form. However, in modern English, "they/them" can be used as a gender-neutral pronoun to refer to a person whose gender is not known, or to a person who does not identify as male or female.
In the sentence "If someone gives me bad advice, should I be mad at them?", "them" is used as a gender-neutral pronoun because we do not know the gender of the person who gave the bad advice.
Using "him/her" would be gender-specific, and it might not accurately reflect the gender identity of the person in question. In contrast, "them" is more inclusive and acknowledges that people of all genders can give bad advice.