Important Safety Considerations

I'll copy what I have written before:

Cancerous cells happen every day in everyone's bodies. It's just a fact of life. DNA gets damaged, and that causes the cell to replicate improperly. Your T cells find those mutated cells, and destroy them. Where it becomes a problem is when your immune system does not recognize the mutations, and does not destroy the cells in time. That is why it becomes more and more likely to get cancer as you age. Your body's immune system gets slow, and gets overwhelmed. Also, the more time that goes on, the more chances there are for DNA damage, along with more epigenetic gene mutations. It's also why people with AIDS often die of cancer in the end. The immune system is the key to keeping cancer at bay.

Obviously growth factors can increase the growth of certain cells in the body. If one of those cells becomes cancerous, and expresses the receptor for that growth factor, then increases in that factor can speed up the spread of that particular cancer. Your immune system is still the gatekeeper in this whole game. A healthy and functioning immune system should be capable of taking those cells out in time. If you do not have a healthy and functioning immune system, or have some genetic predisposition to a certain cancer, then taking compounds that increase growth factors can increase the likelihood that a cancer will spread faster if it gets out of hand. They are not going to cause cancer, though. Human growth hormone and IGF-1 levels are highest in adolescence. However, most young people have immune systems that are just as strong. So cancer is not a problem. There are cases where a genetic predisposition, or an epigenetic change from an outside factor, can tip the scales in cancer's favor. In those instances, taking supplements that increase certain growth factors is probably not a good idea. If I found out I had brain cancer, I probably would reevaluate taking certain things that increase BDNF and NGF. However, I am not going to lose sleep over it under normal circumstances.

Really, your immune system is what is keeping you alive. Without it, you would die in very short order. You can't prevent all cancerous cells. There are just too many instances of DNA damage every day to do that. Luckily we have evolved over millions of years to have systems in place to catch those instances, and remove them from the equation before they can get out of hand. It's when those systems are depleted or overwhelmed that it becomes an issue. You could die from the rhinovirus if your immune system was depleted enough. Hell, you could die from an ear infection, and that still happens in parts of the world. This is why a healthy and functioning immune system is key to ensuring you are protected.

The brain has its own distinct immune system, called the neuroimmune system. The main receptors that control neuroimmune signalling are the chemokine receptors, opioid receptors, cannabinoid receptors, and TAAR1. Glial and mast cells are the primary defenders in the brain, and mast cells can actually mediate signalling to the gut in the microbiota–gut–brain axis. So while most of your peripheral immune system cannot pass the blood brain barrier, your brain also has its own systems for protecting itself. If that system is working properly, increasing growth factors in the brain should not lead to a higher instance of cancer. However, genetic variations and epigenetic changes throughout life can alter that susceptibility, and alter the functionality and efficiency of those protection systems. So OP's caution is certainly warranted, as it gets very complex. If you have a family history of brain tumors, particularly Glioblastoma and Astrocytoma, don't take things that increase NGF and BDNF. It's not worth the risk.

TL;DR: Growth factors do no cause cancer, but they might increase their spread if one's immune system is not functioning properly and destroying them before they get out of hand.

Not to add any more confusion to the equation, but sometimes NGF lowers the propagation of certain cancers as well.

Nerve growth factor abrogates the tumorigenicity of human small cell lung cancer cell lines

Nerve Growth Factor Exerts Differential Effects on the Growth of Human Pancreatic Cancer Cells

Also this: Nerve growth factor: role in growth, differentiation and controlling cancer cell development

Overall, these studies indicate that the only presence of NGF is unable to generate cell carcinogenesis, both in normal neuronal and non-neuronal cells/tissues. However, it cannot be excluded the possibility that the co-expression of NGF and pro-carcinogenic molecules might open to different consequence. Whether NGF plays a direct or an indirect role in cell proliferation during carcinogenesis remains to demonstrate.

So merely the presence of NGF does not generate cell carcinogenesis. However, NGF does promote angiogenesis, which worsens breast cancer.

Nerve growth factor promotes breast cancer angiogenesis by activating multiple pathways

Nerve Growth Factor Stimulates Proliferation and Survival of Human Breast Cancer Cells through Two Distinct Signaling Pathways

So, like everything else, it's complicated...