Does seeking to live a healthy lifestyle show God that I don’t trust him to heal?
A: Not generally, but that is somewhat of a personal question based on the motives of the heart. As Christians, we should see ourselves as stewards of the bodies God has given us. This would necessitate a healthy lifestyle.
Consider finances. God provides all that we have. We are meant to trust Him for the provision of our daily bread. That said, you would not think it godly to squander all your funds every day on consumer pleasures because God has promised to provide for you.
Or consider your personal holiness. God has saved you and forgiven all your sins by the blood of Jesus Christ. It is not your good behaviour that will get you to heaven; rather, it is the righteousness of Christ imputed to you. But Paul makes it clear that it does not give license to sin all you want (Ro 6:1).
In the same way, just because God heals the body, or even that he will give you a new one in heaven, it doesn’t mean that it would honour him to abuse your body now. So, it is right to live a healthy lifestyle for his glory and for the health and energy to serve him in whatever ways he has called you to.
That said, some are obsessed with what they can do. There are myriad weird diets and lifestyles that become almost a religion for those that practice them. Check your heart on this. Do you trust God as you seek this lifestyle? Or do you trust in the lifestyle?