Does my stepson who has power of attorney over my ex-husband have the right to say who can and cannot visit him when he lives at home?

If your husband suffers from incompetency then he may if he lives with him in his own home, decide who can visit and who cannot. This most often happens when the POA sees the visitor as someone who is upsetting to the elder, or trying to in some way take advantage of the elder or abuse the elder. If you are the ex wife and wish to visit with your ex husband now as a friend it may be a very good thing to form a solid relationship with his son who is the lion at the gate. Offer him help with cooking, light cleaning, some respite so he can shop or get a break. Make yourself invaluable and helpful and that will keep your foot wedged in the door. I hope you will have good luck and will update us on what works for you. I think it is good you want to be supportive.

If the PoA is legally active (meaning, your ex is now incapacitated and has a medical diagnosis as such which meets the criteria to activate the PoA), then yes his son can do this. In this case you have no power.

If you think the son is somehow abusing or neglecting your ex then you report him to APS (and expect to possibly never be able to see your ex again -- especially if the report has no evidence) or you take your evidence to an attorney and expect to pay for those services.

Technically, legally yes.
If a visit upsets someone then the POA can prohibit visits from those people.
If you want to visit talk to the POA and ask. Nicely.
If he refuses you can ask if you can have supervised visits. He can allow that or reject that as well.
I think the fact that this is your ex-husband limits your standing with your (ex)-step-son when it comes to requesting visits.