If you're selling something, especially on Facebook Marketplace, it's good to be able to accept payment for it in as many ways as possible. The reason for that is simply making things easy for someone to give you money. Often times it's a hassle for you, requiring time and sometimes money in order to make it easy for a customer.
So you have to ask yourself if it's worth it? Speaking for myself, I don't take credit cards. I just didn't want to go through the hassle and expense of doing that. Of course, my graphic design business isn't retail, so I always figured that I'd be OK with that. I also don't accept cash. If someone wants a cartoon or design from me, I accept PayPal and Chase QuickPay. I've accepted PayPal for years, and I bank at Chase, so they're easy for me.
So you could consider limiting what you accept. Yes, you're going to lose people who want to pay you with a system that you don't accept, but that's a risk you take.
If someone has sent you money through Facebook Messenger, or any other system that you're not on, the money will simply sit there, and then will go back to them. They made the mistake of beginning a transaction before checking with you. And no, they won't lose their money, it will just stay in limbo until it comes back. Each system has a different time for that, but they're all the same. If you try to send something that can't be accepted, it gets returned.
So really, it's up to you. If you think it's worth your time and trouble to set up an account in a particular money-managing app, go ahead and do so. It's all done online, and there's really no person you can talk to you to help set it up. If you'd rather not do that (and I defend your right not to), just say "Sorry, I don't accept that". Businesses do it all of the time.