What is in your purse? wallet?
Why not make it a habit to check the contents of your wallet every day before you leave the house. If you are not going to use a credit card that day, take it out of your wallet and put it in a safe place. If fact, you might rethink your use of a wallet. What do you really need to take with you? Probably for most days you can eliminate almost everything except some pesos and FM2/FM3/FMM and emergency phone numbers. Any why leave the credit card in a wallet? If you need to use it that day, some of the small cell phone fabric cases will work in protecting your card.
For women - rethink your use of a purse. What do you really need that you must carry in a purse? Why not empty your purse on the kitchen counter and look at each item - and ask - "when did I last use this item that required it to be in my purse." Now that it is cooler, you can even stash a comb, lipstick etc in your car. If your purse is large, downsize it to something small that you can wear cross shoulder. Another option would be a fanny pack. Better than a large purse, but still not the perfect solution - which is to go purseless.
It is one way to keep your possessions - let the pickpockets and mustard bandits decide to pass you by