Some people are just addicted to the feeling of being right and dress it up as concern. It’s up to the individual to figure out which it is and decide to disengage or not.
Sure, but considering this is a frequent accusation atheists level against Christians in general, I think we Christians are under an extra obligation to make the charitable assumption that someone else really means what they say and has our well-being in mind.
We’re not accountable in front of God for how cleverly we figured out who secretly hated us here on earth. We’re accountable to God for how charitable we are to others, from our very hearts and minds.
Pragmatically speaking, at the very least, no situation is popping to mind where I’d literally tell a Protestant: “You don’t
really care about me! I fundamentally disbelieve you have inwardly good motives! I am going to walk away from you but it’s
your fault!” We might largely disengage if conversations seem unproductive, but no need to have an actual confrontation about it. One possible downside of such a confrontation might be that, even if we’re right, being called on it might make someone too uncomfortable to later come back to us (if they have a very fragile ego and don’t know yet how to say ‘sorry’).
I reckon staying as accessible as possible to as many people as possible for as long as possible is best. So when the OP asks for advice on how to “refute” the idea that the Protestant genuinely has concern for him, that’s what I’m counselling against here. It’s just the wrong road to go down, in my opinion. At least taking their concern at face value keeps the connection open, and the Protestant might still benefit from that connection, if we entrust it into God’s hands.