Is the print on eggs safe for consumption?
This is an excerpt:  


  Regulatory compliance. Inks used for egg coding must comply with
  government regulations governing food marking inks. These broadly state
  that inks printed on food items must be safe for human consumption,
  both when the food item is raw and when it is cooked. Egg coding must
  not weaken the egg shell or penetrate through the shell. Once dry, the ink
  should remain on the egg shell and not contaminate the egg during the
  cooking process. 


Now, that is taken from this link which is actually an advertising pamphlet by a company selling their printing service, but it should be true for commercial products. If a small farm is stamping their own, then it might be worth questioning them.

I would expect to see more and more eggs getting the inkjet treatment as more countries are making it a requirement, not just acceptable.  One would assume this is to prevent practices like carton swapping and relabeling of old product.  Myself, the only eggs I have purchased with it on also happened to be in red and it was only logos, not date and tracking info.  They did not do a good job with the fast drying aspect as the logos were smeared on some eggs, but when the eggs were boiled it did not fade or further smear.  There are multiple food safe inks, often meat and meat products are inked thought typically on fat, skins or casings, but candies, baked goods and such are expanding that practice steadily.  I am not sure what type of inks they are using as soy based food grades any I have seen tend to smear and wash off.  I can only hope since these are food agency approved and even required in some places they were reasonably tested.