I think that, technically, it's rude to put a note like that on the invite. It strikes me as being somewhat akin to writing "no children" on a wedding invite. Technically, these people are adults and should be expected to know that they need to stay at home if they realize that they're sick. The rudeness comes in assuming that they are so lacking in social niceties that they would go to a Meet the Baby party while deep within the throes of a nasty cold.
Of course these people are
so lacking in social niceties that they would show up sick...
I know you said there wasn't another date until October, but is there a way that you can put some info on there about an alternative date? Something like "In light of this being a particularly virulent cold and flu season, mom has set aside $date for folks who are sick on $partydate to meet the baby." Then you're being informative, not telling them what to do.
Even though you're still telling them what to do.
Are there a couple of people who you could deputize? If I had a relative who I knew would have the gall to show up all germy to meet an itty, bitty baby, I would tell them to stay home if I realized that they were sick. It might help to take a couple of the relatives who DO have some social graces aside and ask them to keep an eye on the most likely offenders.
You should also be on the lookout at the party itself to make sure that anyone who does manage to show up sick doesn't hold the baby.