Door will open for everyone on the server, why?

You are right, use Local Script. The reason why this does not work as a local script is because you probably put it into the workspace, instead, put it into StarterPlayerScripts and change variables from script.Parent to workspace:WaitForChild("What you need here") (Wait for child because it might not replicate when the script runs in starter player)

local rc = 5000
local debounce = true
workspace:WaitForChild("Door1").Touched:Connect(function(hit)
    if hit.Parent:FindFirstChild("Humanoid") then
        local player = game.Players:GetPlayerFromCharacter(hit.Parent)
        if player.leaderstats.Cash.Value >= rc then
            if debounce then
                debounce = false
                script.Parent.Transparency = 0.5
                script.Parent.CanCollide = false
                if rc.Value <= rc then
                    script.Parent.Transparency = 0.15
                    script.Parent.CanCollide = true
                end
            end
        end
    end
end)

neither this worked

I know this might seem odd, but a pretty simple way to set this up is to use the PhysicsService to isolate a group of allowed players from the group of disallowed players. If you are aware of how to use the service, that's good. If not, here's a brief explanation of what it does and how useful it can be.

Basic initialization:

local PhysicsService = game:GetService("PhysicsService")
-- Now you create the collision groups. These can be named anything you want.
PhysicsService:CreateCollisionGroup("Name1")
PhysicsService:CreateCollisionGroup("Name2")
-- etc.

By creating collision groups you are starting to set up what can collide with something or what is unable to collide with something. The PhysicsService is very useful for making certain models be able or unable to collide with one another.

So now, because the PhysicsService only takes BasePart instances in its collision groups, you need to loop through the player's Character and enter every individual part into a collision group. Something like this, you might think:

for i,v in pairs(player.Character:GetChildren()) do -- player can be defined through something else, like PlayerAdded or GetPlayerFromCharacter()
    if v:IsA("BasePart") then
        PhysicsService:SetPartCollisionGroup(v, "NameofGroup")
    end
end

The door that you seek to set collidable can be added to the second group, if desired.

Next is a basic function of the service called CollisionGroupSetCollidable(n1, n2, bool). This function sets the collision of n1 and n2 to the value of bool, which must be either true or false. I'm pretty sure you can figure this one out by yourself.

Now, I personally don't seek opposition to using a local script, but in my opinion, you should use PhysicsService over client-sided CanCollide. It makes your life that much easier.