I had the opportunity to speak with several native speakers, It's fun, and they learn my native language, the problem is that several of my language partners speak with an American accent and the others in a British accent. It gets complicated for me; I mix spellings and pronunciation. I do not like this, I read in a site that I must choose an accent. So, if I choose a British accent, do I have to stop talking to all the Americans I've met?
I think the advice you received means to pick one accent to learn and use yourself when speaking. The point of this is to simplify your learning. If you have to learn two different ways of saying everything then it will take you a lot longer to reach proficiency. There are many other places where English is spoken with other accents as well (Australia, Canada, New Zealand, South Africa, etc), and different accents within each country. It's not realistic to expect to learn them all.
This doesn't mean you can't communicate with others who use a different accent. American and British people speak together all the time. They usually understand each other quite well when each is using their own accent. The even enjoy hearing the other accent sometimes. The same goes for Americans from the south and north or people from different parts of Britain.
There are differences between ways people in each country speak that go well beyond just the accent. These difference sometimes even confuse native speakers, but the more we are exposed to the other way of speaking the less we are confused. This will happen for you, too.
For the purpose of including all of the wisdom in the comments, I'll say that I agree that it's not necessary to emulate any one accent perfectly. The most important thing is to speak with good grammar and convey your meaning correctly. It's alright if you sound like a non-native speaker. Very few English learners ever get completely rid of of their foreign accents, even after years of living in an English speaking country.