No. Apple makes it difficult and expensive to make software backward compatible with old versions of the OS. (More specifically, you can only write for old versions of the OS if you use the old software development kit, which means you are unable to use newer features of the OS including security items. Intuit chooses to use the current SDK.)
You can use Turbotax online with Firefox or Chrome, if your version of Safari is also outdated. Or you may need to use an alternative company.