I have am the full custodial parent, can my ex legally take our children out of state without my consent?

Idaho typically is a joint custody state which allows the party with custody at the time to go anywhere with the children, including out of state. If you have joint custody then your ex probably has the right under your court order to have unrestricted visitation/custody of the children. I agree with MTG that if your ex lived in Utah at the time of the divorce then there is no question that he would be entitled to take the children to Utah.

If, however, he moved recently then you are looking at a change in circumstance that may alter the provisions of your custody order. You may have a custody order that is not practical with him living in Utah (i.e. weekly exchanges of custody). If he is entitled to every other weekend, then there may not be a change in circumstance. Idaho courts/judges do typically make the moving party pay all transportation costs and usually do not restrict movement of a parent unless it alters the custody arrangement or impacts the best interests of the child. http://idahodivorcelawyer.blogspot.com

Generally, the non-custodial parent needs permission to take the children out of state.  However, did your agreement take in to account that you ex lived out of state and that visitation was granted anyway?  In other words, if the visitation schedule was established while he was already a Utah resident and the court and you were aware of it then I doubt that you have an recourse to complain now.  If, however, the change in residency was recent then I would seek to modify your agreement based upon the change and as you see fit.  You ex can also make the same application.