I don't have much trouble with the concept of Marian apparitions, for the simple reason I've had a number of spiritual experiences of my own viz. my father appeared in my room the night he died (despite not knowing where I lived).
He apologised for a lifetime of deliberate cruelty in which he destroyed my self confidence and damaged my mind, we talked and argued, and at the end he gave this terrifying scream and disappeared.
There have been others as well, although that one was unique.
I'm Catholic now, but my old Protestant (Presbyterian) pastor once said to me about Marian apparitions "There's been a lot of them... They (approved apparitions) line up with Scripture...I think they're a judgment on a divided church...".
I've had a handful of visions of the pastor too since he died. He turns up, says something which is quite relevant, and then just disappears again.
So I don't have a problem.
Then there's the miracles which accompany them. In the case of Fatima for example, there were three distinct miracles. The first was the "dancing sun" although it should be more accurately called "the terrifying sun". The 70,000 witnesses thought they were going to die at times, burned up by a sun which appeared to be heading straight for them. At least one hectoring atheist was bought to his knees in abject terror.
There was the fact that 70,000 people stared at the sun for about ten minutes straight, and it didn't even hurt their eyes. Usually you can't stare directly at the sun for more than about ten seconds without risking eye damage. I drive for a living, and I know how strained my eyes get if I don't wear sun glasses. Those people were protected.
Then there was the business of hours of rain saturating the ground and the witnesses's drenched and mud spattered clothing. Suddenly in an instant, the ground and their clothes were dry, and their clothes were clean. It seems scientists calculated the amount of energy required to vaporise that amount of water was about the same as a ten megaton nuclear weapon.
But they never even felt it. Just suddenly realised everything was dry and clean.
God was looking after His witnesses, having sent His Mother to three semi-literate children in a poor Catholic country, one of Europe's backwaters at the time. Two of them died within a couple of years, leaving only one remaining witness. Yet somehow, despite this unpromising start, like Christ being crucified as a criminal in an occupied country with no official written record, the message got out, and stuck, like His words which He said "will never die away".
And as the old pastor said, Fatima lined up with Scripture -
Matthew 11:25 NIV At that time Jesus said, "I praise you, Father, Lord of heaven and earth, because you have hidden these things from the wise and learned, and revealed them to little children.
What were the wise and learned doing? In 1917 they were in charge of a war which was killing young men by the million. And one of Mary's warnings was that if men didn't change, there would be another worse war, and we all know what happened then.
You could even extend her warning to today.
So on account of my own spiritual experiences, the fact these approved apparitions line up with Scripture, and they're backed up by miracles, I don't have a problem with approved Marian apparitions.