Oh, yes, I remember this case. There was a little flurry of publicity about it, not too long ago.
The Jewish obligation is to post the mezuzah, as there is a clear commandment for us to do so. There is a concept of dina d’malchuta dina (the law of the land is the law), which states that as long as no Jewish law contradicts it directly, one is obligated to follow the laws of the land. However, this is not a case of dina d’malchuta dina since in fact, a condominium or tenant board is not the law of the land, and indeed there is a commandment to post a mezuzah, so that would not be relevant.
Although initially I had thought that given the general understanding that has prevailed of the first amendment1 (later extended to state and local governments, via the fourteenth amendment2) this would make a difficult court case for the tenant organization, in fact, it’s not so clear-cut how it would turn out. Actual court case outcomes seem to have been somewhat more mixed than one might expect. In the aughts there were a couple of legal battles (one in Illinois, and one in Texas) that went back and forth in the courts, but both ended up with the condo associations working something out with the resident, and in Illinois, Florida and Texas, the states passed laws to protect Jews from mezuzah bans. There was an attempt at a federal law, which didn’t pass.
Nevertheless, at the very least, it seems unlikely that a condo could get very far without a lot of bad publicity, and certainly although in some cases courts ruled against the tenants, eventually in all the cases, the tenants eventually either won, or worked something out with the tenant organizations.
That being the case, in her place, I would suggest trying to explain to the condo association that it is a religious obligation and not optional. Unless there are other, underlying disagreements (such as a feud with a neighbor, or perhaps someone on the board), it seems likely that something can be worked out.
I suspect you may also be interested in the larger question - what if this had been a case where a Jew was coming up against an actual law. I would like to give you a good general answer, but un/happily (depending on whether you like complicated or not; I do, but not everyone does) one would have to present this on a case by case basis with a rabbi knowledgeable about halacha (Jewish law). The general rule is that when the Torah commands us, we are obligated, but the specifics of a given case might offer alternatives that allow some sort of compromise, or one might discover that in fact, what they had thought was an obligation turned out only to be a custom, or any number of other possibilities.
1 “Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.”
2 “All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the State wherein they reside. No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any State deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws.”