Whenever I try to replace blocks such as fence gates, trapdoors, etc, the replaced block state is always in its default state. If there is a way to keep the same states, please inform me. I have searched everywhere for a solution but could not find an answer.

Unfortunately there isn't a proper option yet for keeping the state properties and just changing the block type.

But you can use any state in the replacement by "copying" that state either from the schematic or the world with Alt + middle click while in the Rebuild mode, and then use an empty main hand in the Rebuild replace operation. This will then use the "copied state" in the replace operation. So if it's for example a stair in a certain orientation and connection state, you would need to place it in the world in that correct state and then copy that state.

It's pretty cumbersome for blocks with lots of states and a proper "fuzzy replace" or "block type replace" operation is definitely planned.