For written language yes, spoken it doesn't really matter as people will cut you a lot of slack.
In Spain there was a football comentator from England, Michael Robinson. Robinson had an obvious English accent and even though his Spanish was very very good, but he still he messed some things -including genre- and nobdy cared. He was a comentator for many years and people liked him a lot.
In the US you have other examples of the same things. For instance I can think of Sofia Vergara and Charo to name the first that come to my mind. Both quite popular and I can spot their accent and some mistakes instantly and I'm not even a native speaker.
Also I mess gender a lot myself when I speak English and people don't seem to care.