In the following question "Orthodox Visits to Other Denomination Sanctuaries" it discusses whether one may go into a Reform or Conservative synagogue for prayer and/or a wedding. Is one allowed to go into a Reform or Conservative synagogue to take a SAT test? Most likely the test is not taking place in the sanctuary.
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The SAT seems somewhat analagous to voting:
The question has already arisen about whether one can vote in a church, a place that most consider to be a place of idolatry. It appears that voting in a church is acceptable if necessary (also here), and so long as the voting doesn't occur in the sanctuary.
Now, if voting (which I argue is like taking the SAT) is ok in a church, then how much the more so should it be permitted in a synagogue, again assuming it is not in the sanctuary? The case hasn't been made that Reform or Conservative Judaism is idolatry, and even if it were made, it must surely be less so than Christianity, which elevates a human to divine status -- so if you can go into the church basement to vote, why not the synagogue basement to take the SAT?
Rabbi Dov Lior of Kiryat Arba instructs Orthodox Jews to steer clear of participating in any events held by Reform Jews and prohibits entering their synagogues.