Leviticus 19:19 says: Ye shall keep my statutes. Thou shalt not let thy cattle gender with a diverse kind: thou shalt not sow thy field with mingled seed: neither shall a garment mingled of linen and woollen come upon thee. (KJV)
These prohibitions against mixing things were in the context of having the Israelites show God's holiness. The first prohibition seems to speak against crossbreeding different stocks, and says nothing directly against incorporating tissue from other species into humans. However, even the prohibition as it reads doesn't always seem to have been followed. Why do I say this? There are seven verses in the Bible that include the word "mule." (II Sam. 13:29, 18:9, I Kings 1:33, 38, 44, Psa. 32:9, Zec 14:15) Mules, as we now use the word, and, presumably, as it was used in the Old Testament, are a cross-species hybrid, between horses and donkeys, which sounds like a "diverse kind" to me. Some research with the Blue Letter Bible indicates that the I Kings 1 verses translate the Hebrew pirdah as mule, and that this Hebrew word occurs nowhere else in the Bible, so it is doubtful if it meant anything but a mule, at least here. All three of the uses in this chapter are commands given by King David, to have his son, Solomon, ride David's mule to his coronation ceremony. There is no indication here that God abhors mules. On the contrary, this one was used for an important ceremony, with religious overtones.
If crossing horses and donkeys did not earn God's wrath in Old Testament times, my guess would be that incorporating pig tissue into humans is not prohibited, in and of itself.
A question that should be asked about any proposed scientific development is "what is the motive?" If the motive is self-promotion, bring about someone's destruction, unjustly taking advantage of other people, or destroying a significant part of God's creation, any type of human endeavor, scientific or otherwise, is suspect.
Using pig pancreas cells in a human to help her with a diabetic condition should have been motivated from a desire to help her live a reasonably normal life. I hope it was.
There have been more questionable uses of cross-species tissue growth. An article in New Scientist, Feb 28, 2004, "Art, but not as we know it," reported on the artist, Laura Cinti, who placed cells producing human hair into cacti, where they were able to produce hair, at least for a time. (Only the response to the first question posed to Cinti is now available freely, here. You can pay for the rest of the article.) This may have been mostly self-promotion, and therefore seems suspect, but I don't want to get my blog into the field of art criticism.
When smallpox vaccination, using cowpox germs to engender an immune reaction to smallpox, which is antigenically similar, was first proposed, there were complaints that this was unnatural, and cartoons showing humans with cow's heads growing out of their bodies. Most people now take the use of non-human tissue for medical reasons as a matter of course. (However, the development reported in the post by Catez is different, in that this procedure uses living pig tissue, not merely materials produced by a pig, cow, or bacterium, in a human.)
If the decision were up to me, I'd say, prayerfully, that God gave us abilities to help others, and put us, at least temporarily, in charge, and that transplanting cells from a different species into humans, to help them with a medical condition that doesn't seem remediable by other means, is acceptable.