Will my store have a chance to compete without paypal as a payment option?

Then they are very naive. The vast majority of people who refuse to use PayPal anymore are ones who were on one side or the other of a dispute. There is no more protection using PayPal than there is with any other payment processor and there is definitely less "security" (PayPal accounts are constantly hacked by fraudsters). In fact, there is less protection, since, according to many, PayPal intentionally ties up the process for many months, not siding one way or another so that they can hold onto the money and earn interest off of the money in dispute.

But in a sense, you are right. There are plenty of people out there who are dumb enough to believe anything PayPal tells them. Again, though, this is why I say that people who have to rely on PayPal as a payment option may not be the best (i.e. smartest) people on the planet to do business with. Some of them definitely are pretty good at attempting fraud, though, and you are right because PayPal often lets them get away with it. We have far more fraud attempted through PayPal (as a percentage of sales) than we have with people who use a real payment processor.

Oh, and as a vendor, do not necessarily believe that the "protection" offered by a PayPal confirmed address always protects you. They will try everything possible to get out of that guarantee and if nothing else, will hold up your money for as much as a year.

No matter who your payment processor is, we recommend getting very good at detecting fraud or using a service like NoFraud that will guarantee every transaction. Although fraud is pretty rare in most niches, it does happen and if you are selling expensive items, it can really hurt when it happens!