“Also you shall say to them: ‘Whatever man of the house of Israel, or of the ger who dwell among you, who offers a burnt offering or sacrifice, and does not bring it to the door of the tabernacle of meeting, to offer it to the Lord, that man shall be cut off from among his people.
‘And whatever man of the house of Israel, or of the ger who dwell among you, who eats any blood, I will set My face against that person who eats blood, and will cut him off from among his people. For the life of the flesh is in the blood, and I have given it to you upon the altar to make atonement for your souls; for it is the blood that makes atonement for the soul.’ Therefore I said to the children of Israel, ‘No one among you shall eat blood, nor shall any ger who dwells among you eat blood.’
“Whatever man of the children of Israel, or of the ger who dwell among you, who hunts and catches any animal or bird that may be eaten, he shall pour out its blood and cover it with dust; for it is the life of all flesh. Its blood sustains its life. Therefore I said to the children of Israel, ‘You shall not eat the blood of any flesh, for the life of all flesh is its blood. Whoever eats it shall be cut off.’
“And every person who eats what died naturally or what was torn by beasts, whether he is a native of your own country or a ger, he shall both wash his clothes and bathe in water, and be unclean until evening. Then he shall be clean. But if he does not wash them or bathe his body, then he shall bear his guilt.”
What Does It Say?
Leviticus 17 is mostly given over to laws concerning the shedding of animal blood. The earlier part of the chapter deals with God's command that all animals killed be brought to the tabernacle as a sacrifice. This is specifically mentioned as a means to prevent demon worship in verse 7.
I'm going to read into the text a bit, but the logic seems to be that you have to keep track of all the animals killed. If people are out killing animals however and whenever they want, it's a lot easier to offer sacrifice to a false god. But if everyone has to bring the dead animals to the tabernacle, it's harder to offer an animal as a burnt offering to Moloch or whoever.
This commandment (and all the further prohibitions dealing with animal blood) are extended to any ger living in the camp. And it's interesting that this law deals specifically with the camp and the tabernacle, meaning that it's a law that's specifically already in effect during the 40 years of wandering. This would imply that there are already ger living in the camp who are not native-born Israelis (certainly Moses' wife would be one).
Also of interest here is that these laws would prevent ger living among the Israelites from worshiping their gods with sacrifices. So whatever religious freedom would theoretically exist in Israel would not extend to animal sacrifice or consuming animal blood. It also does not exempt ger from cleanliness laws, such as the need to be ritually purified after touching the carcasses of animals that died of natural causes (verse 15-16).
These verses also seem to imply that circumcised ger still count as ger. After all, no uncircumcised male would be permitted to offer sacrifices to God at the tabernacle. So the fact that both the natives and ger are required to bring their sacrifices to the temple implies that ger with access to the tabernacle are still considered ger.