How can I get this script to not affect Humanoids?

That is pretty simple, actually. Just check at the onclickdown function if a FindFirstChild search in the part's parent returns nil.

local bin = script.Parent
local bp = Instance.new("BodyPosition")
bp.maxForce=Vector3.new(math.huge, math.huge, math.huge)
local movecon = nil
local bpfixcon = nil
function onchanged(prop, mouse)
if bp.Parent ~= nil then
if mouse.Hit ~= nil and mouse.Target ~= nil then
bp.position=mouse.Hit.p-(mouse.Hit.lookVector*bp.Parent.Size.Y)
end
end
end

function onclickdown(mouse)
if mouse.Target ~= nil then
if mouse.Target.Parent:FindFirstChild("Humanoid") == nil then --The new if statement, done before everything else must be done. I put it here instead of onchanged so it does not waste time doing things and generally avoid issues and trolling by spamming click on soneone.
if mouse.Target.Anchored==false then
if bp == nil then
bp = Instance.new("BodyPosition")
bp.maxForce=Vector3.new(math.huge, math.huge, math.huge)--bp.maxForce*700
bpfixcon:disconnect()
bpfixcon = bp.Changed:connect(fixbp)
end
bp.Parent=mouse.Target
bp.position=mouse.Target.Position

if bp.Parent.Parent.ClassName~="Model" then
mouse.TargetFilter=bp.Parent
else
mouse.TargetFilter=bp.Parent.Parent
end
movecon = game:GetService("RunService").Stepped:connect(function(f) onchanged(f, mouse) end)
end --New if statement's end
end --Your script is exactly the same on this point on
end
end

function onclickup(mouse)
bp.Parent=nil
mouse.TargetFilter=nil
if movecon ~= nil then
movecon:disconnect()
movecon=nil
end
end

function fixbp(prop)
if bp == nil then
bp = Instance.new("BodyPosition")
bp.maxForce=Vector3.new(math.huge, math.huge, math.huge)--bp.maxForce*700
bpfixcon:disconnect()
bpfixcon = bp.Changed:connect(fixbp)
end
end

function onselected(mouse)
--movecon = game:GetService("RunService").Stepped:connect(function(f) onchanged(f, mouse) end)
mouse.Button1Down:connect(function() onclickdown(mouse) end)
mouse.Button1Up:connect(function() onclickup(mouse) end)
end

bin.Selected:connect(onselected)