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.
The SAT seems somewhat analagous to voting:
Voting is a civic duty and how we contribute to governance; taking the SAT is required to get into most colleges.
Both elections and the SAT are administered by some other organization; the location used is just a location, not a sponsor.
Choices are very limited. For voting you have to either use your assigned voting location or arrange for an absentee ballot (which may require leaving town). For taking the SAT, locations and dates are very limited and many are on Saturdays, so avoiding the local test location might involve significant travel.
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?