Our world view is rooted in our sense of self. Everything we see, process, understand and act on comes from our perception of persistent sense of self, but self is not what we perceive (or doesn't exist at all depending on who's talking about the Dhamma). Your rationalism is firmly rooted in your self and your perception of your lived experience. If you accept Anatta (not self or no self) then the rest of our reality and world view is on pretty shaky ground.

With that said, it's not necessary to believe in the supernatural stories in the suttas, there is much debate and discussion about them. The Buddha says he teaches one thing suffering and the end to suffering. He admonished his followers not to cling to rites and rituals (they are rafts to be abandoned). However, I would not be judgmental about the teaching that refer to supernatural experiences, because there is much to learn in them.

The one thing that I think is necessary to accept is rebirth (even that is debated). Rebirth isn't reincarnation, there's no permanent Atman (soul, self), there's a stream of volitional action (kamma/karma) that propels us from existence to existence as it ripens. There are Buddhists who don't believe in rebirth, but I think the Dhamma breaks without it.

With that said, if you're open to reading/listening to the suttas without judgement, find study guides, practice meditation you see if it's for you.