Is it safe to invest in mutual funds after retirement?
It's not only safe but also important to invest in mutual funds. You should consider it very seriously, as mutual funds are actually not an asset class but they pave the way for investors to invest in equities and fixed income in a more organised manner.
When you invest in an equity fund, you are able to instantly diversify and somebody's responsible for managing that money. It provides you with the convenience of doing an investment without going to a broker and without doing a lot of learning. In short, you can invest without doing all the hard work associated with investments. So, you get your money managed with convenience.
In the case of fixed-income funds, they are more tax-efficient and liquid. With these, you can get access to something that is otherwise not available to individual investors. Although you can't buy government bonds, you can very well buy a government security fund or overnight or liquid funds. So, you can't avoid mutual funds and I think for most investors, it's a sensible investment choice and an important one.
Plan it methodically and learn a little bit about how to approach it. But post-retirement, if you are not going to invest in mutual funds, you'll be in trouble.