Who is eligible to make a sacrifice?
1. Every single Jew is eligible, man or woman.
2. Jews who are lax on their Torah observances, the idea behind this is that if they come to bring a sacrifice and do teshuva, that will evoke psychological responses in them to want to fix their ways and live a more Torah enriched life.
3. Someone who desecrates Shabbot publically is not permitted to bring a sacrifice.
4. A non-Jew may bring a burnt offering. If he brings a sacrifice to Hashem, this may eventually pull him away from his other false beliefs and accept Hashem’s rule; thereby, leading him to fulfill the 7-Noahide laws- the 7 laws mandatory for non-Jews to follow.
Essentially, we can see that no matter the status of the giver, Hashem is open to creating a relationship with whoever sincerely wants one.