In my opinion the petition has a fair chance of success. Firing several tenured professors as part of policy-change in the academic direction of an academic unit is very damaging, to the fine department of mathematics at VU University Amsterdam and to the entire university. Of course, it is a great injustice to the scientists involved whose positions are threatened. It is reasonable to hope and even to suppose that some reconsideration will take place on all the necessary levels.
The decision will be especially harmful to the prospects of attracting excellent young researchers. Y. Barnea mentioned in a comment above that the university web-page declares about tenured-track positions: "In the event of good performance, the tenure track offers a permanent employment contract, or 'tenure'." This declaration by the university agrees with the international standards of tenure and academic freedom but is not in agreement with the recent move regarding the geometry group. We can hope that the VU University Amsterdam will prefer its own declared policy. I thus suggest to VU: Correct and forget
We can hope and even expect that the decision will be reversed and that the massive support expressed by the petition will find listening ears. I do not support, however, Andre Henriques's approach of "name and shame." We do have to remember that individuals are sovereign to make their decisions and even to make mistakes, and so are departments and universities. The academic community should tolerate and can accommodate mistakes by individuals, and it can accomodate even mistakes by institutions, especially very rare incidences of this kind. If the decision will stay I suppose that the excellent four people whose jobs are threatened will find other good academic jobs that they deserve, and also that UV Amsterdam mathematics department will eventually move on. But it will be much better to the department, to the university and to the academic community, to move on with this issue settled in the correct and just way rather than otherwise.
In my opinion, it is legitimate for people to have opinions, even strong ones, on relative merits of areas of mathematics, to express such opinions, to try to promote them or to try to translate them into academic policies. Such is the idea of basing a department solely on applied mathematics or, on the other side, building it around some specific area of pure mathematics. Not agreeing on such matters is in the heart of academics (and even more so in other areas of academia.) In an academic environment where we are not suppose to agree, keeping the conventions regarding academic freedom and tenure is so much more important.