All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
In our view, it is not permissible to close the mosque in order to prevent the praying people outside the mosque from being led by the Imaam if they could do so on the pretext that the mosque is full of people. The fear of provoking the anger of the non-Muslims that you mentioned is not a sound reason for that. This matter was ongoing for tens of years and there was no general problem or an extreme danger to necessitate issuing a Fatwa to close the mosques or to carry out two Friday prayers in the same mosque.
In fact, overcrowdedness, the lack of mosques and the narrowness of roads are not an excuse for doing that. This matter was ongoing for hundreds of years in many countries and the Muslim scholars did never issue a Fatwa to close the mosques; rather, they stated that the Friday prayer, as well as the eclipse prayer and the prayer for rain could be prayed in the streets for necessity if the mosque is not able to accommodate the congregation.
There is no doubt that holding two Friday prayers in one mosque is not permissible, in principle, even the majority of the scholars prohibited holding more than one Friday prayer in the same town without a need, let alone holdng them in the same mosque.
However, the solution could be in limiting the attendance of the Friday prayer to the congregation of men only and to prevent the women and children from it; as they are not obligated to attend it. Indeed, Ibn Nujaym from the Hanafi School said in his book "Al-Bahr Ar-Raa-iq" that “If the mosque becomes overcrowded, then they may prevent those who are not obligated to perform it (i.e. the Friday prayer).”
Also, it is possible to hold the Friday prayer in other places than the mosques of the town, like holding it in sports halls at times when it is used, conference rooms and the like, as it is not a condition for the Friday prayer to be held in the mosque according to the view of the majority of the scholars. If all this is not possible, and it is feared that affliction and evil could happen due to the overcrowding, and there is no other alternative than to carry it again in the same mosque, then this is permissible for necessity as we discussed in Fatwa 132462.
Allaah Knows best.