I am a young patient with kidney failure and I have no insurance. Is FIRE still possible even with such obstacles?

As long as you can build passive income more than your expenses and have a sizeable emergency cash reserve, you're good.
FI is possible. RE maybe not so. Work as long as you can instead. And you may want to find an employer that has a group medical benefit that covers pre existing illnesses as well. Leverage on that insurance benefit if you can't have your own.

Don't be too agressive with your investments as well. You want less volatility because your illness probably already provides you with all the volatility and suprises in your life. Don't take anymore unecessary volatility.
Stay safe, take care of yourself, earn more, spend less, be smart with your investments. All the best Anon. :)

Yes. Although you may have no insurance and it is unlikely that an insurer would accept you, do not give up on your dream of FIRE. As it stands, you basically need to be very careful about the investments you undertake to achieve FIRE. Insurance is basically plan B should anything go wrong, so if plan B is not available then your plan A must have added safety measures built in.

Some example of added safety are: Have a larger emergency fund. Go defensive when you start investing to ensure that you don't lose your hard earned capital. Make sure your allocation to equities is diversified and that you stick to proven businesses/companies, at a good entry price. Throw in a good mix of bonds/bond funds to reduce volatility in your portfolio. Build up your CPF to prepare yourself for old age. Keep sufficient liquidity. Lead a simple lifestyle (be frugal). Due to the added safety measures you need to take, you may find that FIRE might be delayed a little, but it is still achievable nonetheless.

I wish you all the best in your journey towards FIRE.