Why won't this if statement work properly?

My conclusion on your issue is that you're possibly modifying the wood value on the client.

Remember this:

FilteringEnabled disallows the client from replicating most changes to the server. If you modify a value on the client, the change will not be seen on the server. If you desire client-server communication, use RemoteEvents or RemoteFunctions.

I also noticed you have an error in your if statement:

elseif leaderstats.Wood.Value <= 50 then

The original condition already checks to see if the value is equal to 50:

if leaderstats.Wood.Value >= 50 then

You should replace your elseif with just else:

if leaderstats.Wood.Value >= 50 then
    -- First code segment
else
    -- Second code segment

else will supply the following code in the event that no other conditions pass. Since x >= 50 checks if x is either greater than or equal to 50, there's no real reason to use an elseif because it's a waste of typing when compared to using else in this scenario.

What happens is that on the elseif statement, you say if it equals the same or less, not only less, and with the if statement you're saying it equals the same or more, to fix it, just do

elseif leaderstats.Wood.Value < 50 then

which gives us

game.Players.PlayerAdded:Connect(function(player)
    local ReplicatedStorage = game:GetService("ReplicatedStorage")

    local remotes = ReplicatedStorage:WaitForChild("Remotes")

    local leaderstats = player:WaitForChild("leaderstats")

    local Inventory = player:WaitForChild("Inventory")


    game.ReplicatedStorage.Remotes.BuyHouse.OnServerEvent:Connect(function()
        if leaderstats.Wood.Value >= 50 then
            leaderstats.Wood.Value = player.leaderstats.Wood.Value - 50
            Inventory.BoughtHouse.Value = true
            ReplicatedStorage.Text.Value = "-50 Wood"
            print("Enough coins")
        elseif leaderstats.Wood.Value < 50 then
            ReplicatedStorage.Text.Value = "Not Enough Materials!"
            wait(2)
            print("Not enough coins!")
            ReplicatedStorage.Text.Value = "Press E to open the house upgrade menu!"
        end
    end)

end)