It's no big deal. It's just bodily fluid. My Man couldn't care less. He's still getting laid, a little blood (or a lot) doesn't bother him. I tend to be more horny during my period, and if we can catch it just before the cramps start with a big orgasm, the cramps tend to be less severe.
I actually have maroon towels and a maroon sheet that I put over the regular sheets on the bed during my period. It protects the bed, and we actually can't see just how much blood there was. I do usually like to take a warm bath before hand to stanch the flow a little, but if he gets some blood on him, it'll easily wash off. We might occasionally skip the half day or so when the cramps are the worst or if I'm having a really painful period.
The only day it bothers me a little is the last day, when it's (sorry) kind of brown. We have anal sex a lot, and I'll always say, "That's my period blood, there. It's not something else." He just laughs at my embarrassment. But, I've never been embarrassed enough NOT to do it.
I can't imagine putting a sponge in during my period. Wouldn't it get pushed around and end up behind your cervix? Having had a Today Sponge get stuck, not once, but twice (once necessitating emergency medical attention) I don't want to have to spelunking around in there after sex. It may be fine for some, but we'll just deal with the blood with no sponge.