Kehilat Hadar is constrained by needing to find spaces that can fit all of the people who come to our services - there are not a lot of available spaces in our neighborhood. Generally, churches are available when other spaces are booked. Synagogues affiliated with the Orthodox, Conservative, and Reform movements, in addition to Kehilat Hadar, have all at times met in church buildings.
There are a variety of halakhic sources you can consult about this issue - the following are responsa by Israeli Orthodox rabbis, and written relatively recently:
Yechaveh Da'at v.4 # 45
Tsits Eliezer v. 14 #91
Aseh Lekha Rav v. 1 #59 and v. 4 #53
An on-line responsum about entering churches and mosques from the Masorti Movement in Israel can be found at http://www.responsafortoday.com/vol6/2_1.pdf. It is written in Hebrew, and cites some of the responsa above, as well as other rabbinic and halakhic sources on this topic.
For the most part, the possible prohibition on going into a church comes from the Talmud's concern about idolatry (avodah zarah). However, for the past several centuries, most authorities have not considered Christianity to be idolatry - you can find this in the writings of the Meiri, for example, a famous rabbi and halakhic authority in 14th century Provence. Here's a link to some of what he wrote:
(quoted in an article at http://www.chiefrabbi.org/dd/views.html)
Many modern halakhic authorities have the same perspective. There is also an interesting document written by a commission of French rabbis about Jewish views of Christianity posted on-line at http://www.bc.edu/research/cjl/meta-elements/texts/cjrelations/resources/documents/jewish/France1973.htm that, in section 2, gives a variety of traditional sources indicating that even from the time of Tosafot (early Talmudic commentators) the rabbis have not considered Christianity to be idolatry.
Finally, Rav Soloveitchik, the pre-eminent 20th century American Orthodox rabbi, once said that, although in general one should not go into a church, it would be permissible to go to an auditorium or other area in the church building if you could go in through a door that was not used for going into the church's sanctuary. When Kehilat Hadar meets at the Second Presbyterian Church, we meet in a basement room that is not used for church services, and the door we use to go in is not generally used by people coming in to the church sanctuary for services (there are several doors on that side of the building, and for services the church opens the middle ones up - we use the one all the way on the left).
Meeting in a church building is not ideal, but there are not a lot of free spaces for us to use, so we view this as a temporary solution until we can find something better. For some people, there is a comfort issue with meeting in such a space regardless of what the halakhic sources say, and we certainly understand that.