How can I determine the sex of a tree seedling?
There is absolutely no way to tell to be honest because mulberry trees have the capability of changing sex (reference). From a paper titled "Diversification of mulberry (Morus indica var. S36), a vegetatively propagated tree species", I quote


  The sex expression of plants appears to be a function of hormonal
  control; there seems to be evidence that dioeciously plants (male and
  female reproductive organs on separate plants) are potentially
  bisexual and that a delicate internal hormonal balance results in one
  sex "over-riding" the other. A traumatic incident might, therefore,
  act by temporarily upsetting this balance, which is later restored in
  a way that leads to the opposite sexual character being manifested.
  Another pointer in this direction is the fact that a variety of
  artificially applied chemical substances has been shown to affect the
  sexual expression of a significant number of different plants. It is
  also reported that some chemicals known as the steroid hormones might
  be a major key to the sex expression lock. Thus, it is
  possible that to "create" a new sex in a plant by either a physical
  shock or a controlled chemical process


They could also have male and female flowers (monoecious) on one plant with most of them being self pollinating (references).

So, in effect, nurseries that are advertising these trees by sex are ignorant or quite plainly taking people for a ride. I would suggest that you plant your seeds and don't worry about it too much since they have the ability to self pollinate. If by bad luck, you find them all male/female or are not pollinating to your liking, go for a tree sex change after consulting an expert on the topic. Here is a basic guide to identifying between male and female trees/branches (reference)



White mulberry male flowers (reference)



red mulberry female flowers (reference)