Statement I: The biblical prohibition against eating pork (Leviticus 11:8 and Deuteronomy 14:8) doesn’t apply in modern times since it was primarily intended to prevent parasitic diseases, such as trichinosis, that can contracted by eating pigs. At most, the injunction should be considered a “good suggestion.”
Statement II: The biblical prohibition against touching a pig carcass (Leviticus 11:8 and Deuteronomy 14:8) doesn’t apply in modern times since it was only intended to prevent ritual contamination ("tumah" in biblical terminology) during pilgrimage festivals when one would visit the sanctuary, which was prohibited to someone in a state of tumah (eg. Leviticus 15:31, Numbers 5:3). At most, the injunction should be considered a “good suggestion.”
Individuals making statement I in the presence of certain Orthodox Jews should do so only if prepared for a vigorous debate. The assertion that some Biblical commandment is “obsolete” due to changing circumstances directly contradicts a major religious tenet - that G-d’s laws are immutable and transcend the rationalizations of mere mortals to explain away. Ritual law, they will say, is just as imperative now as when Moses transcribed it directly from heaven. By the end of the conversation, one would likely run a serious risk of being labeled a heretic or worse, “Reform."
REFERENCED TEXTS:
3 Do not eat any detestable thing.
4 These are the animals you may eat: the ox, the sheep, the goat,
5 the deer, the gazelle, the roe deer, the wild goat, the ibex, the antelope and the mountain sheep.
6 You may eat any animal that has a split hoof divided in two and that chews the cud.
7 However, of those that chew the cud or that have a split hoof completely divided you may not eat the camel, the rabbit or the coney. Although they chew the cud, they do not have a split hoof; they are ceremonially unclean for you.
8 The pig is also unclean; although it has a split hoof, it does not chew the cud. You are not to eat their meat or touch their carcasses.
Leviticus 11:1-8
1 God spoke to Moses and Aaron, telling them
2 to speak to the Israelites, and convey the following to them: Of all the animals in the world, these are the ones that you may eat:
3 Among mammals, you may eat [any one] that has true hooves that are cloven and that brings up its cud.
4 However, among the cud-chewing, hoofed animals, these are the ones that you may not eat: The camel shall be unclean to you although it brings up its cud, since it does not have a true hoof.
5 The hyrax shall be unclean to you although it brings up its cud, since it does not have a true hoof.
6 The hare shall be unclean to you although it brings up its cud, since it does not have a true hoof.
7 The pig shall be unclean to you although it has a true hoof which is cloven, since it does not chew its cud.
8 Do not eat the flesh of any of these animals. Do not touch their carcasses, since they are unclean to you.

Rashi ibid.
(*NOTE* The discussion in the Talmud about touching a carcass from an unkosher animal should not be so obscure, as it immediately proceeds what is probably the most quoted passage in High Holiday Sermons: The "Three Books opened on Rosh HaShana." )
