I just strain with a couple of layers of muslin, then I wash those cloths with a bit of soap and boil them up. In earlier years I didn't boil them every time, but I wasn't as lazy about washing them immediately then. We test our milk on city children when they come to visit and none of them have been sick. ;-) If you were pregnant, I guess you'd want to be a bit careful about raw milk and we always tell people when we serve them our dairy products that they're unpasteurized, in case they have an immune system issue/pregnancy we're not aware of. I'm only that careful because we can't test to ensure there's no problem. I have no real doubts though, because we ensure everything is scrupulously clean and store the milk carefully.
(When our cow had mastitis, the first indication was the sliminess of the straining cloths when I put soap with them. That was a very useful day-by-day indicator.)
The full benefit of the colostrum to the calf, in regard to the immunity it confers, passes after the first few hours. After that it's just an extra-good feed and as you've said, the cow has way more than the calf can eat, so it won't matter much if you take some.