Apart from what I think of it, why do you consider it bothersome? Isn't it rather that you are bothered by them
confronting or bothering you with them seeing meaning in every coincidence? Very small difference, I admit, but an important distinction to be made in my opinion. Either way, why do you let yourself be bothered by it?
For me, it is not so much that I see some grand meaning behind every coincidence. I just consider them to be beautiful. It has a certain "magic" to it. In a way, all of life is one big coincidence (and isn't this the same as stating there is no coincidence?), but regarding those more "obvious" coincidences this becomes, well, more obvious.
It "emphasizes" the beauty of life/reality to me, you could say.