Apparently eating the meat of calving/recently calved cows isn’t a good idea… why?
I expect you should kill the beast first. 
Apart from that, well firstly, the animal is under some stress and secondly it’s obviously not yearling beef.
But these conditions aren’t exactly unusual and I can’t recall any basis for the assertion. I suspect somebody’s having a lend of you. You have a cite?
I have never heard anything about meat from reproducing cows being bad for you healthwise. But for eating it most likely would not be as pleasant of an experience. Cattle meant for the food market are usually fed in order to make cuts of meat more tender and more flavorful, while reproducing cows would be fed the right nutrients for the best health of their reproductive system. From a business standpoint you invest time and money in reproducing cows with the goal of getting many calves over a period of years. Only older animals or ones with reproduction problems are sold for the food market, and usually only ground beef, roasts and other low value cuts are made from them.
Upton Sinclair mentions it in “The Jungle”
I worked in an abbatoir for over a couple of years. It wasn’t uncommon to get what the slaughtermen jovialy referred to as ‘slinkies’ from time to time. A slinky of course being an unborn calf. The calves were sent along a special chute for processing for the skin, which is apparently highly values leather. The carcasse itself I assume ended up in the ‘hoof and horn’ hopper. The cows themselves were broken down exactly as any other beast.
In other words there is a fair chance that you have eaten the meat from pregnant cows and never knew it.
As Slartibartfast said, this is not a desirable situation for all sorts of reasons, not least of which is that you are slaughtering reproductive stock. All good farmers these days make sure they preg test their cows to ensure that full cows aren’t sold accidentally. Ocaasionally of course one slips through the net. In times of drought, low prices or the break up of a farm full cows will be knowingly sold. Usually these go to the market as full cows and command reasonable prices. However if conditions in a region don’t favour herd buildup they will be bought by abbatoirs.
Don’t sweat it. There’s absolutely nothing physically worng with eating pregnant cow. It doesn’t make for prime beef, but a lot of the stuff we were putting through was far from prime anyway. Just hamburger and pet food in the making.