do_not_dump.rb

class DoNotDump < Module
  class << self
    alias [] new
  end

  def initialize *ignored_ivars
    super() do
      define_method :marshal_load do |pairs|
        pairs.each { |ivar, value| instance_variable_set ivar, value }
      end

      define_method :marshal_dump do
        instance_variables.each_with_object [] do |ivar, pairs|
          pairs << [ivar, instance_variable_get(ivar)] unless ignored_ivars.include? ivar
        end
      end
    end
  end
end

example.rb

class Example
  def initialize
    @unserializable = ->{}
  end
end

Marshal.load Marshal.dump Example.new
#!> TypeError: no _dump_data is defined for class Proc

class Example
  include DoNotDump[:@unserializable]
end

Marshal.load Marshal.dump Example.new
#=> #<Example:...>