This is not an easy decision to make in many cases.
When one side is pro se, it is often considered an automatic thing that the unrepresented side should have a “support person” with them to make them feel more comfortable. The decision should never be automatic.
In mediation, confidentiality is extremely important to the process. Even if outsiders sign the confidentiality agreement (and there should be one in all mediation), they have less motive to adhere to it than the parties to the dispute at hand. Even if everyone agrees to letting them participate, I require them sign the confidentiality agreement.
That is why when I am acting as the mediator, I never make the decision without obtaining the position of the other side. They may have real misgivings about letting an outsider participate, no matter how well-intentioned, hear various settlement proposals and being given access to personal information.
The other issue to consider is that frequently the party to the mediation will not be the real “decider”. Frequently the spouse or some other person will have to be persuaded to give their assent in order for an agreement to be concluded. In that case, having them participate may make very good sense and enhance to possibilities that the mediation will result in a settlement agreement that will not be upset or attacked later.
Some mediators consider an attorney representing a party to be an “outsider” who should not participate absent the permission of the other side. That is a fairly extreme view. People have the absolute right to counsel in all phases of mediation in my view, as long as that attorney is there as their legal representative in the matter.
It is always good for the parties to tell the mediator and the other party or parties that someone other than a party will be attending the mediation. This gives the parties a chance to consider the position they will take on the issue. The requesting party may feel that this is just a chance to prepare arguments against the attendance of a non-party. I would suggest that it is a chance to persuade the other parties that it is a good thing that will help achieve a settlement. Popping the issue on people at the very beginning of the mediation session will more than likely result in a reflexive “no” to the request.