بسم الله الرحمن الرحيم
The ruling of Eidgah is just like mosque in respect of waqf, but in other rulings it is not like mosque. An unclean man or women experiencing menstruation or post parturition bleeding (Nifas) may not enter into mosque as well as it is makrooh to smoke in mosque, but the women experiencing menstruation or post parturition bleeding may enter into Eidgah. It is sin to talk unlawful in Eidgah, but you should offer salah in Eidgah itself.
Allah knows Best!
Darul Uloom Deoband
This answer was collected from the official ifta website of Darul Uloom Deoband in India.