Rhonda, Mexicans and Mexico has nothing to do with this, I find that comment completely repulsive.
This is your baby, if you don't want him touched, just say it and walk away. Rude is your right. She is rude for thinking that she can do that to anyone's baby. Some cultures revere children, and have the need to show love and affection to anyone's child. If this is not your cultural way, then everyone needs to respect that. Nut job or not. There are normal people in the world that dont do this, and then there is 60 year old, emotionally unstable women who think using a strangers baby or acquaintance baby as a doll, is ok. Maybe someone else let her do that to theirs with out incident so she probably thinks its ok. Next time she comes around, do the basketball thing. Block her. Twist and turn and as your do it you say "sorry today she cant be held. She has a cold" if it continues. Be blunt with no emotion. Just simply tell her. NO. Doesn't sound like your losing a whole lot if she doesn't like you any more. One of those things that is better that she avoid you, cant have everyone love ya, even at church.
I have no problem if people, tickle, or hold my babies hands or feet. If they want to goo goo at them, or make cutsie faces. I do have an issue if they grab and want to hold my baby with out first getting permission, or even making a pleading face to do so. Only once, did a distant cousin want to do that, at my mothers funeral. When she was done, and saw my face, she immediately apologized and said she has a bad habit of doing that cause she loves babies. She is a NICU nurse, so I can forgive her for that but it is very uncomfortable when those things happen.