Prior to death, a revocable living trust is transparent for tax purposes. The trustor (the person creating and funding the trust) hasn’t genuinely given up ownership of the assets because he or she can revoke the trust at any time. For this reason, the tax law ignores the existence of the trust. Income produced by the mutual funds will continue to be taxable to that individual, just as they were before the mutual funds were put in the trust. Similarly, the existence of trust would not alter the individual’s ability to claim a deduction for real property tax on the home. Nothing changes.
After death, the answer depends on provisions of the trust. The possibilities are too varied to summarize them without knowing more.