Where do Christians stand on the topic of consuming "unclean" animals?

Unfortunately, the question didn't specify which denomination this person belongs to, or where she got the (incomplete) idea of what is or is not considered biblically clean.

Of those listed, these are all biblically clean animals:

• Buffalo is similar to beef.
• Venison, Elk, and Reindeer (Caribou) are all types of deer.
• Pigeon is type of dove.

Regardless of one's denomination within Judaism, Christianity, or Islam, all of those meats should be acceptable.
(But if some people simply find the thought of eating Rudolph, Bambi, or Bullwinkle unpleasant, then that's up to them to decide; it's personal taste, not a religious matter.)

Within Christianity, the doctrines on what meat may or may not be eaten vary greatly.

Most mainstream denominations totally ignore the matter.

Some though, do restrict themselves to meat only from biblically clean animals.
Here is an informative booklet (also available as a free hard-copy) on the subject published by one such denomination. It should answer all your questions and more:

• What Does the Bible Teach About Clean and Unclean Meats? | United Church of God

Others, like Seventh Day Adventists, are even more strict and try to be vegetarians, but do allow individuals to occasionally eat meat, but again only from biblically clean animals (e.g. no pork or shellfish).

Christians find in the New Testament but one stance with regard to the eating of any kind of meat. The ancient laws of the Old Testament were fulfilled in Jesus Christ. Christians are told in the New Testament that laws about (for example) circumcision no longer apply to followers of Jesus because theirs is now a spiritual circumcision of the heart, not a literal, fleshly procedure. Consider this point, as it leads on to other laws such as the dietary ones for those in the Old Covenant (Testament).

"And ye are complete in him, which is the head of all principality and power: In whom also ye are circumcised with the circumcision made without hands, in putting off the body of the sins of the flesh by the circumcision of Christ. Buried with him in baptism, wherein also ye are risen with him through the faith of the operation of God, who hath raised him from the dead. And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses; blotting out the handwriting of ordinances that was against us, which was contrary to us, and took it out of the way, nailing it to the cross. Having spoiled principalities and powers, he made a shew of them openly, triumphing over them in it. Let no man therefore judge you in meat, or in drink, or in respect of an holyday, or of the new moon, or of the sabbath, which are a shadow of things to come, but the body is of Christ." Colossians 2:1-17 A.V. [Bold emphasis mine]

The only other passage about eating certain meat is in Acts 15, regarding whether to eat meat that had first been presented before an idol in the meat market. It is a matter of conscience for Christians. A person with a weak conscience might be stumbled if they saw a Christian eating meat that had been presented first to an idol, before the Christian bought it for personal use. A mature Christian would know that an idol is nothing, and have no qualms, but to avoid stumbling a weaker brother, they might do better to take that into consideration. It is a matter of personal conscience. The only requirement stated in Acts 15:19-21 is not to eat meat where the creature had been strangled (as its blood would not have been drained out of its body). Blood was never on the menu for Jewish people; from the start, they were not to drink it or to eat meat where the blood had not been poured out on to the ground. I know where I stand on that point (some might think I have a weak conscience) but I say nothing about it to others who have a different view.

I know where I stand on the matter of eating meat, and whether the animal had split hooves or not has nothing to do with it. Other Christians take a different stance. But Colossians 2:1-17 forms the basis of my stance.

There are no food restrictions within Christianity, the restrictions in question refer to Leviticus 11:3-4 (NIV),

You may eat any animal that has a split hoof completely divided and that chews the cud. There are some that only chew the cud or only have a split hoof, but you must not eat them. The camel, though it chews the cud, does not have a split hoof; it is ceremonially unclean for you.

Basically much of your list describe unhoofed animals and camels also definitely fall into this category because its explicitly listed and rationale for the prohibition described, which is specifically on your list. Crocodiles, kangeroos and wild boar are restricted, they are unhoofed and/or don't chew their cud.

I am not sure about the deer and horse (zebra) families and I would guess they are regarded as 'clean'. Israel definitely used chariot combat and they'd need 'clean' horses for that, i.e. defilement would be touch as well as eating.

Pigeons should be okay, the Israelites in the wilderness ate quail and was a key part of their sacrificial system. Snails I don't know (probably not), locust however are permitted (Leviticus 11:22).

However, whilst there are no food restrictions for Christians ("...all food is clean" Romans 14:20), the Apostle Paul clearly warns us to be very mindful of this specific issue (Romans 14:20-21; NIV),

Do not destroy the work of God for the sake of food. All food is clean, but it is wrong for a man to eat anything that causes someone else to stumble. It is better not to eat meat or drink wine or to do anything else that will cause your brother to fall.

Some Christians are very particular about food restrictions and many are especially concerned about alcohol consumption and we should be duly diligent.