The noble Shaykh Muhammad ibn Ramzan al-Haajiree (May Allaah preserve him) was asked about the permissibilty of inviting the non-muslims to the 'Eid salaah to listen to the khutbah as a form of da'wah.
[Q]: Is it permissible to invite the non-muslims to attend the ‘Eid khutbah?
[A]:The Shaykh (May Allaah preserve him) said:
This is permissible. The hukum is for everyone to attend the 'Eid prayer and sermon, and in the time of the Prophet (sallalaahu ‘alayhi wa sallam), the kuffar would enter into the masjid and it even took place that a few of them were tied to the pillars in the masjid of the Prophet (sallalaahu ‘alayhi wa sallam). There is no problem in the kuffar attending the 'Eid sermon, although we should be careful not to imitate them in the way they conduct their gatherings.
Now I want to mention something important that is common in the non-muslim lands, and that is that some people say they don’t have a musallah, so they gather the people in a big area. However, if this area is used by the disbelievers for their gatherings and celebrations of shirk, then it is not permissible for the muslims to use the same area. There is a hadeeth where someone approached the Prophet (sallalaahu ‘alayhi wa sallam) and said “I made an oath that I would slaughter in a particular area.” The Prophet (sallalaahu ‘alayhi wa sallam) questioned him: “Are there any idols worshipped in that area?” The man said “no!” The Prophet (sallalaahu ‘alayhi wa sallam) further asked him: “Are there any gatherings from the days of jahiliyyah that are celebrated in that particular area?” The man said “no!” This is a proof that if any of these two particular affairs are present in that area, then it is impermissible for the Muslims to gather and perform their 'Eid there. ‘Eid is from the open legislated forms of worship.
[taken from a tele-link session with Shaykh 'Muhammad ibn Ramzan al-Haajiree (hafidhahullaah) and the brothers at Mpubs, Tobago on August 16th 2012]