Why does my door change orientation while opening?

The problem is that the CFrame values have a rotational value imbedded into them, and when you create a CFrame this value is set to 0,0,0. To change this value you can use CFrame.Angles().

This is an example that lets you understand the context and syntax:

CFrame.new(0,0,0) * CFrame.Angles(0,90,0)

However, if you test out the code you will see that the Y value won't be 90 degrees. This is because CFrames use radians instead of regular degrees.

2 Pi is equal to 360 degrees in radians. This means that 1 pi is 180 degrees, pi/2 is 90 degrees and so on. Roblox has a function that converts regular degrees into radians, as well as a function that does the reverse.

math.rad() expects a value (in degrees) and converts it into radians, neat!

math.rad(180) -- outputs pi's value

Here is your script with this implementation:

local model = script.Parent.Parent
local door = model.Door
local TweenService = game:GetService("TweenService")
local scanner = script.Parent
local info = TweenInfo.new(
       2,
       Enum.EasingStyle.Exponential,
       Enum.EasingDirection.Out,
       5,
       false,
        0





)
local drzwizam = {CFrame = CFrame.new(33.95, 3.49, 24.98) * CFrame.Angles(math.rad(0),math.rad(0),math.rad(0))}
local drzwiodw = {CFrame = CFrame.new(33.95, 3.49, 31.462) * CFrame.Angles(math.rad(0),math.rad(0),math.rad(0))}
local tweenotw = TweenService:Create(door, info, drzwiodw)
local tweenzam = TweenService:Create(door, info, drzwizam)

scanner.Touched:Connect(function(card)
    if card.Name == "Handle" and card.Level.Value == 1 then
        print("gud card")
        tweenotw:Play()
            wait(1)
            tweenzam:Play()
    end




end)

However, since I don't know the full context of this door you'll have to change some of the values yourself. Good luck!

TweenService:https://developer.roblox.com/en-us/api-reference/function/TweenService/Create

Nothing seems wrong with you script but I edited some parts:

local model = script.Parent.Parent
local door = model.Door
local TweenService = game:GetService("TweenService")
local scanner = script.Parent
local info = TweenInfo.new(
       2,
       Enum.EasingStyle.Exponential,
       Enum.EasingDirection.Out,
       5,
       false,
        0





)
local drzwizam = {CFrame = CFrame.new(33.95, 3.49, 24.98)}
local drzwiodw = {CFrame = CFrame.new(33.95, 3.49, 31.462)}
local tweenotw = TweenService:Create(door, info, drzwiodw)
local tweenzam = TweenService:Create(door, info, drzwizam)

scanner.Touched:Connect(function(card)
    if card.Name == "Handle" and card.Level.Value == 1 then
        print("gud card")
        tweenotw:Play()
            wait(1)
            tweenzam:Play()
    end




end)