Well, I think there are 2 separate threads going on here.
Firstly, the actual relationship with the priest. Yes, priests have a special role in the Church, but they are still human beings. A priest has made a commitment to love everyone and serve God by tending His human flock. A married man has made a vow to love and honour his wife and protect his family. In short - both have made vows to commit to a way of life. So…if the OP would find this kind of affection wrong from a married parishoner, she should also realise it is wrong from a priest.
However, friendship is a beautiful and wonderful gift. The big problem I see is that a relationship that one knows deep down can’t actually lead anywhere lends itself to a kind of distorted glamour: a sort of feeling that precisely because it can never be - every moment shared becomes acutely precious and painful at the same time. It’s not a real relationship and just like porn, it can spoil and undermine the joy of a real, true courtship and marriage. That’s the thing to guard against as far as I can see: that a (platonic) relationship with a man who is held up as an example of goodness and kindness, who feels obliged to listen and help - can become some kind of emotional security blanket and shield from the big, nasty world. That’s when falling in love (or lust) becomes a danger. This is especially so, if the OP is a sensitive soul who worries about what her fellow parishoners are up to!
I am going to stick my neck out about the parishoner who she has a problem with. Parishes are funny places. Single women can and are treated with suspicion at times and anyone who says not is either deluded or attends an amazing parish! I don’t doubt her assessment of the situation as far as this person is concerned at all - not one bit!
If this person was genuinely concerned for her soul and a compassionate human being, perhaps he and others might have befriended her, made her welcome and accepted that she had a desire to be part of their community and serve God. Maybe if she had been made to feel more welcome, she would not have felt such a deep, personal affection for the priest (perhaps he really is the nicest person in the bunch)
The Parish Priest is not the only person responsible for a thriving and friendly parish. It is the responsibility of every single one of the parishoners. Perhaps the priest recognises that some of his flock are rather cliquey and critical and feels like a bit of an outsider himself…well, that’s created a tinderbox, ready to set alight, hasn’t it? All it needs is a young, attractive and vulnerable young lady with a shared interest…
What does this ‘pillar’ of the community do? Does he raise the matter with the priest? No, he puts further strain on the situation by going up a level and creates an atmosphere of suspicion and guilt. Not sensible, considering!
I hope the priest and the OP are recieving sensible, compassionate support from somebody. My advice would be to find a different parish and remove yourself from the situation and my advice to the priest would be to talk to a fellow priest he could trust and get some support and guidance on his vocation (even if that might mean re-evaluating whether he is cut out for his role)

As an aside, we grew up next to the Methodist manse and one of the resident Ministers (they came on 4 year rotations) came without his wife, as she remained close to her elderly parents. He often confided in my mother that the female attention he received was embarassing! Several woman seemed to be battling it out as to which of them ‘took care’ of him the best, from baking him cakes, to popping round for tea and a chat. Of course, that lead to an atmosphere of suspocion and jealousy amongst them and he wasn’t that popular with their husbands either!!!
I am sure nothing improper actually happened - again, I suppose for many of the ladies, it was a man who had to be compassionate listener and always polite and basically a professional ‘good bloke’ so it was a safe environment to fuss over a charming man!
He did once, jokingly, ask my mum how priests managed!
On the flip side, another incumbent was married to a nurse, who was the ward sister where our PP spent some time. After the expereince, at an Ecumenical meeting, he remarked how great it was to be woken up each morning by a smiling lady with a nice cup of tea! The Minister laughed and said yes, but (along with the Anglican Vicar) they told him that both their churches were constantly being bled dry financially by divorce settlements, because so many wives found it impossible to cope with having a husband who was constantly ‘in demand’ for displays of warmth and generosity - and so many other women felt they had a ‘right’ to his time.
I think being the wife of a minister of the Anglican or other churches with married clergy is a vocation in itself.