Maybe, maybe not, aluminium dissolves into both cold and hot when the food, or drink, in a vessel made of it, is acidic. So you certainly get more aluminium into your body if you use pots made of it. But there doesn't seem to be any officially admitted studies that would prove that kind of amounts are dangerous to your health. Not if you are a healthy adult anyway. Seems it can cause something like dementia, but when eaten that is claimed to mostly become a concern only if your kidneys don't work well.

But because of those studies aluminium seems to be used in lots of things from where it may end up in our stomach at least in very small amounts, like cans, food packaging in general like the lids for dairy products like yogurts, tin foil is actually mostly aluminium foil these days, aluminium blisters for packaging medicines and so on. So we get a lot of exposure anyway.

And one thing you find when it comes to the potential toxicity in the amounts humans now regularly are exposed to is the good old "more research needed".

Because of all the other exposure if you want to play it safe avoid that kind of pots, but it is not certain they are a problem.

I need to get to work so I didn't have time to read this all through, but one long article:

https://pmc.ncbi.nlm.nih.gov/articles/PMC2782734/