Yes, you can date while divorcing, but whether you should is a very different answer. Of course like most areas of law "it depends" on the facts. For example, in an ultra-simple uncontested case with clean asset division, no children of the marriage, each person financially independent, no anger issues on either side then perhaps the answer is to just be considerate of the other person's feelings and pursue your romantic interests.
However, my typical answer is that if you are going to date while divorcing try to be discrete, don't go where your mutual friends go, leave the pics and comments off of social media and make sure that you are fulfilling your obligations while the case is pending both financial and related to your children.
Most judges (as in almost all) will say to keep significant others (S.O.) away from the children especially if there is a custody dispute or they are younger and have not already met the other person (horse out of the barn argument). Kids have a hard time with their parents' separation and adding other people into the family dynamic does not make things easier in most situations. When clients tell me that all they did was go to a backyard BBQ or to the beach with their kids and the S.O. and perhaps that person's children as well it tends to inflame the other parent in the divorce. I have had parents tell me how much their kids want to play with the SO's children....ughhh not a great idea.
The goal is to get your divorce final and not create drama and new issues to antagonize each other about. If a party has to pay child support, spousal support or maintain household bills and carrying charges nothing is worse than the court finding out that gifts, meals and vacations took place with the SO but that the court ordered obligations were not met.
Likewise, if a party wants spousal support and is already living part-time with another person or is discussing publicly future marriage plans, of course that may affect the negotiations as well as any judicial determination about the need for spousal support. Likewise, it can also create the appearance that the party obligated to pay can do so with ease because they are already living with an SO who has good income.
The last reason is that one person may seek to delay the finality of an agreement and try to hold up the divorce as leverage for a better deal.
Therefore, while difficult, it is best to put relationships with new people on the back burner until the divorce settlement is signed. If in doubt, you should consult with your divorce attorney for guidance.