What mental issues can delay transitioning?

I have anxiety and depression (which I think was caused by my gender issues) and I'm afraid that when I'm older and plan to transition, this will delay it. I'm going to a CAMHS appointment on the 6th and I'm planning to get some help with it, assuming they'll help.

However I'm worried that I'll be denied stuff when I'm older just because I was diagnosed with depression or anxiety.

This won't cause any delays, right?