Earlier quoted context omitted.
While it's true that people that want to understand you would understand you, even if you speak wrong, it's not something "not to worry about". Using the wrong gender or articles quickly gives a hint that you are some lowly educated factory worker living in Germany for 20 years and not caring to learn the language.
I agree. Probably it's good to know that it doesn't matter, just so that you feel less fearful and tend to speak more, even wrong....
Native German speaker here: I disagree with all the sentiment of "less fear". Better concentrate on your ability to formulate grammatically correct sentences.
In school, I often felt that the German grammar works somewhat like a mathematical proof system (and asked myself why German grammar is not part of math classes). When studying mathematics, you first have to learn to write correct proofs. It makes no sense to try learn something more deep in mathematics if you have difficulties writing elementary proofs.
For German, it is the same: first learn the internal structure (grammar) of the language (just like predicate logic in mathematics) and just like thinking how to express something that you want to prove in predicate logic, find out how to formulate something in German's grammatical structure.
Only after this elementary step, you can begin with more complicated things.