If the shul sanctions breaking halacha, it is not a kosher shul. If it does not, only the people there happen to not keep halacha, then as long as the services are done in a way that is al pi halacha, one may daven there. To define what is al pi halacha, learn shas and shulchan aruch or ask your rav.
The built on Shabbos sheilah is a separate sheilah, it has nothing to do with the fact that it is a shul. Depending on whether they told them to build it on shabbos or the builders just did it on their own and some other factors, it would be assur or muttar to enter any such structure, and you should ask your rav.