I feel weird going against the grain here, but actually I find including that wording on the invitation (or anywhere in the envelope) to be rude. On one level it's insulting to assume that adults won't know they ought to stay home when they're sick, without being told. On another level, since you know these people won't stay home when they're sick, I feel doubtful they would take the extra warning to heart or realize it was directed at them.
My personal opinion is, if you're going to host a party specifically so people can meet your new baby, it ought to be set up so people can actually, you know, meet the baby, as in hold, touch, and interact with. If you're inviting people to your house to meet your new baby, and then only one designated person is allowed to hold the baby while everyone else stands eight feet back with a face mask on and waves at the child--well, if I was at a party like that, I would wonder what the point was, and why the mom didn't wait until she felt more confident about the child's/family's health before having a party. Or why she was having a party at all--why not invite people over in small groups, where she has more control?
OP, I know this isn't your baby but your SIL's, and she's set on having a party on a specific date. In that case, I think the most you can do is greet people at the door, assess who's showed up sick, and then warn SIL, baby's father, etc. so they can swoop in and cheerfully keep the baby from being held for too long, if at all, by those rude, clueless people. I'm assuming simply not inviting the potential offenders is not an option.
I apologize, I'm honestly not trying to be snarky or anything, I just feel like I'm completely missing something here (which would not be the first time). I don't blame people for being worried about the flu, the news coverage has been terrifying; but in that case, I say don't have a party at all, rather than have a party and make everyone feel like their health is going to be scrutinized and judged if they attend.