As long as one is in good health, there is no problems with donating blood. I know that the Red Cross screens pretty carefully any more. Any trips to Europe seems to be pretty much disqualifying because of the mad cow disease. Yet, they don't consider certain medications or trips to the Middle East a problem.
I spent virtually all of the Eighties and more than half of the Nineties in Europe. And I ate a fair amount of English beef (the original source of Bovine Spongiform Encephalopathy (mad cow disease)).
The Red Cross smiles tolerantly at me, then politely shows me the door when I have the temerity of asking if they want my blood this time.
It's been a long time since i've donated (in Berlin in 1986 or so, IIRC), but generally they keep an eye on you while you're donating and shortly afterwards. They'll offer juice and cookies to get the blood pressure up a bit and if all is well, they send you on your way with their thanks.
Some people have a hard time -- get nauseous, cold sweats, even pass out. But that doesn't happen all that often. If you're healthy to begin with, you should be fine.