Hi, I will be traveling to Taiwan at the end of May and beginning of June.

Hi, L.
Currently, it is hard to tell the exact weather for May and June. Generally speaking, the rain will not so much at the end of May. But it will become hot, so the sun glass and suncream are necessary.
I still suggest you take your rain gear, because it may easily rain on the island comparing to your country.
Have a nice trip ~