Eh, I never had an issue. I would leave an inch left in the bottle, then once done with my beer swish and drink the remaining yeasty beer. Worst case I may have farted a little bit more than normal - or I may have just noticed my farting more thinking it may have been attributed to the yeast. Regardless, it was never bad at all. I never had nasty ****s from it.
Actually, I used to have bad allergies and got sick a lot (mild sickness, don't feel well, cold/sinus type crap). As soon as I started drinking homebrew over 2 years ago, it's been the healthiest I have ever been. Same with my ex. She was always sick for days. She is never sick anymore, neither am I. I'm not saying I am immune to everything, but I think it had strengthened my immune system. Worst that has happened to me is I ate something bad, felt like crap, took one, felt completely fine shortly after.
Cliffs: It's good for you. Drink it all up.
I've supplied homebrew to many, many parties and people. Bottles and kegs. I rarely used fining agents (I forget, or it's a dark beer and I don't care). My family has literally got trashed off my beer (bi-annual reunion), when everyone woke up the next day everyone felt great. I have never had a single complain about my beer giving someone the farts or ****s. I've had many friends and strangers get trashed off my beer too. Drained 35 gallons one night.. You and your friends will be fine, and actually feel better.
Also, no pathogens can survive in beer, so you can't get an actual sickness from beer. There was a study where they injected beer with E-coli. It died in a matter of hours or days, depending on the concentration, the latter being fairly high.