Consider that there are a significant number of people who don't know they have more relatives than the ones they know and love. If the information is public, it becomes an avenue for blackmailing.

Scams about relatives already happen without DNA [1].

Depending on what state in which you live your insurance coverage or cost might change too. [2]

There's also significant risk that your DNA will be sequenced in one jurisdiction but, because of The Cloud, it gets analyzed and stored in another jurisdiction. For example, the EU and US have very different privacy laws.

Some DNA analysis software employ stochastic algorithms. That means that the answer they provide can be different if run more than once, especially if run with different parameters (such as sample pool). [3] [4] Some customers know this and will ask for their data to be reanalyzed.

Some companies make the DNA available to be downloaded by the customer. That file can then be used for your own analysis or research. It could also be uploaded to other companies for different analyses or conclusions.

I don't think it's unreasonable to assume that your grandmother, who uploaded her DNA to a foreign company for a new or different analysis, has given a foreign adversary private information about you and your potential medical hazards or secret relationships.

[1] https://www.khou.com/gallery/news/investigations/consumer/vi...

[2] https://www.cnbc.com/2018/08/04/4--risks-consumer-face-with-...

[3] http://mathgen.stats.ox.ac.uk/impute/impute_v2.html

[4] http://www.genetics.ucla.edu/software/admixture/