These types of offers happen, although they are not the norm. If it was here in California, what you could do is send a counteroffer proposing to accept it, still keep it as an active listing, and give these buyers first right of refusal.
First right of refusal is in the case of another buyer comes who along & doesn't have a contingency to sell their home, then you would give the current buyers the option of dropping that contingency or you are going with the new buyers who are ready to buy now.
Back when I was a real estate agent I noticed that these properties were put into a different section of the MLS called "First Right of Refusal", not even in the "Active" section, and so perhaps new real estate agents who aren't too MLS-savvy wouldn't think to check there for potential homes to show their clients... but if you are saying in your MLS it still shows as "Active" but a little notation next to it, and not put into an entirely different category, then all agents should still see it, but then you have to deal with the dense agents & buyers who'd just automatically write off a listing like that (but those probably wouldn't be the serious buyers anyway in my opinion).
I don't think the buyer could just back out of buying your home unless a contingency couldn't be met - such as selling their home first, can't get approved for a new loan (which perhaps if they can't sell their home they can't get approved for a new loan, hence an additional reason for that contingency), your home doesn't appraise for the purchase price, they find something in their home inspection they don't like, etc. A NJ real estate agent would know for sure.
If I was you, I'd also make them get their home inspection done, and proceed with their full loan approval/appraisal, etc. as if those items are going to be blow the deal anyway I wouldn't want to finally wait until their home sells and then do it. I wouldn't want to wait until they have an offer finally accepted on their home, or even their home sold, before starting all of that up, as it's possible they could have a quick sale and then my transaction would be the one everyone is waiting awhile on - I want to it go bang-bang, done. By requiring my buyers to do all of that, I'll really know if they are serious or if they are just tire kicking.
Then I still have the right to review other offers the entire time, and if one comes along without the contingency to sell their home first, even after my current buyers have gone through their entire process, I'd have some leverage.
I would ask your agent how other agents will perceive the status of your home on the MLS with the letter designation next to it. If your agent was showing you homes to buy, would that affect if they would show you a home or if you would want to make an offer on it?