Are we still liable for accidents if we grant our neighbors beach access with our stairs through neighborly accommodation?

Yes.

Contact an attorney. You should carefully spell out their rights as a revocable license. You do not want this to end up in court because they are asserting an easement by prescription or an adverse possession claim down the road. The license should hold you harmless from any claims and offer you full indemnification if someone is injured using your property. Contact an attorney for assistance.

I WOULD SUGGEST THAT SINCE YOUR INSURANCE DOES NOT WANT YOU TO GRANT ACCESS TO YOUR STAIRS THAT YOU NOT DO SO. IN THE ALTERNATIVE I WOULD RECOMMEND THAT YOU CONSULT WITH AN ATTORNEY TO DRAFT LEGAL DOCUMENTS PROTECTING YOU.

You will still be liable.

The only way to protect yourself is to have your neighbors purchase insurance to insure the use of the stairs and name you as a named insured on that policy.

There is no possible way that this query can be answered in this forum. Find local counsel and retain them (i.e., hire) to do the research and provide you with a detailed memorandum of law on the issue.

Certainly, granting your neighbors permission to use the stairs to avoid them acquiring a right to use them is a useful first step. However, that does not address the issue of liability. You should consult a real estate attorney about drawing up an agreement which would cover the permissive use as well as the liability issues. Your neighbors should be willing to share in this cost, if not then denying access as required by your insurance company will save you litigation in the future.

Short answer, as the property owner you may be liable for injury if it occurs on your property. That's why the insurance company told you not to allow neighbors and their guests to use your property, especially stairs. The best way to prevent injury from happening is to prevent any access by your neighbors. If you still want to allow access you should require your neighbor to indemnify you and hold you harmless from any dispute, lawsuit or potential lawsuit over an injury arising from your neighbor's use, or any guests or family of your neighbor's use, of your stairs. As to your question about whether the neighbors will ever have a "claim to that piece of the property," the answer is probably not. What you are referring to is an easement and easement's generally need to be created through a writing. However, there's something called a prescriptive easement which can be created without a writing but only if certain conditions are met, the most important of which may be the hostility requirement. Under this requirement the use of the easement must be without the property owners permission. This doesn't appear to be the case here. You should take your insurance company's advice and you should also speak to a real estate attorney to understand whether or not your neighbor's use of your stairway will ever create a claim to your property. What I have provided to you are merely general statements, and without all the facts to your specific case, should not be relied upon by you.

That does not free you of liability.