Ok, I'm gonna have to say this is the hardest part for most people. No body I know of likes replacing cords. It's worse than doing the laundry. And, throwing 40 to 80 bucks away each time to get new cords and wait for them to get mailed to you is not fun either.
So, most people opt for the synthetic bungees that last longer but off gas and don't have the "pop" at the bottom of the bounce like the latex type. But, having 2 to 3 times the life of a latex is something to consider especially if on a budget. I personally like the latex since any flatness at the bottom of the bounce really bothers me. Lighter weight people don't usually get the "bottom out" feeling on the synthetic bungees since they rarely overstretch them. So for a heavier person, they might have to ask themselves if changing 2 sets of cords a year costing up to 160 bucks a year is worth the little lack of comfort and G force that they will lose. Note: many people are buying cheap bungee rebounders, the ones around 150 bucks, and putting latex bungees on it.
If someone is really sensitive to off gassing and any petrochemical smells, if buying a synthetic bungee cord rebounder, make sure you know what type of synthetic it is made of. The most common is neoprene. This is used the most. These have a more tensile strength and feel tighter, less stretchy, than the latex type but don't break as much when overextended, especially with heavier people they last way longer. Neoprene also doesn't deteriorate as quick like the latex type in sunlight.
If someone really wants to see if they can tolerate the smell of a synthetic bungee, I recommend getting a single cord and sending it back once you have smelled it.
Note: be aware of companies claiming they use natural rubbers. This can mean that they use a mixture of synthetic rubber mixed with latex. Many people are getting confused and thinking its 100% pure when they see latex. These companies are saying their cords are made of latex but fail to tell you 90% of the cord is isoprene or neoprene. Why should someone have to buy a bungee rebounder and not find out till they get it? It just frustrates me that I had to find all this out on my own since I couldn't get answers from companies selling rebounders. Maybe they don't even know. But, it's not cool that they won't do the research to find out for themselves. Don't they care about the rebounders they are selling. Half of the people I talked to didn't know English so that made it hard too.