Meaning and connotations of "ignorance"

I'm interested in the more intricate meanings of the term "ignorance". In my experience, it is being used primarily to express someone's state of not knowing. Somebody can be ignorant and innocent of it at the same time.

In German, the same word exists ("Ignoranz"), but with a different approach: It describes someone's conscious decision to ignore the facts - usually that's a facet of arrogance (or, less often, stupidity). It's more a description of attitude than state. Not knowing is only the result of it. In any case, you cannot be innocent of "Ignoranz".

Does the same subtext exist in English? If not, what would be a better match for the German word?

A possible English phrase to match the German meaning would be "willful ignorance"--you were given an opportunity to educate yourself but purposely chose not to learn anything new about the situation, preferring to remain entrenched in your current opinion.

Partially.

The word ignorance, (and the adjective ignorant) purely imply a lack of knowledge, understanding, awareness, education, or unenlightened.

It is used both for those who are ignorant harmlessly, by virtue of lack of exposure, and as an insult or negative comment about someone who displays a lack of enlightenment on an issue when they should know better; quite often when they do know better, but choose to ignore the facts. The latter use, as an insult to show contempt for a person is more common these days, often as an alternative for bigoted.

When people "choose to ignore the facts", that fits with the subtext you mention, though when I say that, the person in question usually does not believe the facts to be true. So it is not a case for them of arguing that "black is white", they believe in the opinion they hold; but others do not and think they should not. Usually the division in this form lies in the definition of what is "politically correct".

If someone knew that they were wrong, but doggedly refused to change their opinion, we would say they were stubborn, bullheaded, pigheaded or obstinate. The word pigheaded in particular is used for the bigoted form of ignorant, as it is common to refer to bigoted people as pigs - usually preceded by some negative adjective, e.g. sexist pig.

English can actually make the distinction OP refers to simply by using different inflections...

Your ignorance of a situation means you don't know about it.

Your ignoring of the same situation means you know about it, but choose to ignore it.

As others have said, if you don't want to use the gerund, you can speak of willful ignorance - but the "not knowing" meaning associates so strongly with ignorance that this usually means you have gone to some trouble to avoid knowing (rather than that you know, and choose to ignore).

"Ignore" and "ignorant" come ultimately from a Latin word "ignosco" < "in-gno-sco", meaning "not know". In English the verb "ignore" has come to mean a deliberate not-knowing; but the adjective "ignorant" does not have that implication.

In French, in contrast "ignore" does simply mean "not know", without this implication.