This is a sensitive argument, at least in the US.
As is noted, both pronunciations are ancient and were commonly mixed. In the US, for historical reasons, the /aks/ pronunciation was more commonly spoken in the south than the north, and the /ask/ more commonly spoken in the north. The pronunciation /aks/ has for the most part died among white speakers in the South, but is quite common among African-American speakers throughout the country (who migrated away from the south after the abolition of slavery).
In America, the African-American dialect is heavily stigmatized, and many otherwise racially conscious people, both white and black, will say quite ignorant and nasty things about it. In particular, some white Americans say /aks/ to make fun of the black dialect. Therefore, I strongly recommend that you not adopt it into your speech as a non-native speaker, as you will create serious problems if you are misinterpreted as doing this. Of course, if your accent is strong and you are obviously foreign, people will give you the benefit of the doubt, but it's ground I would not want to tread on. (If you are yourself black, you won't be misinterpreted as racist for saying /aks/ instead of /ask/, but racist people might make fun of you for it.)