In my opinion, it depends on your goal. I mean if your goal is daily communication, for example, you just need to learn like a baby, listen and repeat. However, if your goal is going to university, for your job or something like that, grammar is so very important. 

It bothers me sometimes when native speakers use poor grammar, because in certain situations it isn't appropriate and if you are a native speaker you should know better. It sounds a bit lazy.

But with non-native speakers I don't really mind if their grammar is wrong in places. Native speakers will notice if you get things wrong, but if it doesn't hinder communication I don't care. Pronunciation and being clear when you talk are more important.

In my caase, the answer is <em>YES</em>. 

It's not because I seriously studied English grammar at my schools. Actually I did but I don't expect same thing to others.

Well, I said <em>Yes, I really mind others grammatical mistakes. </em>However, I also would like to say it really depends on others English levels. Since my English lvel is not advanced, I still make a lot of grammatical mistakes when I use English. I already may make some mistakes here.

My point is, if people totally ignore English grammar, it's hard to understand for their conversation partners.

Of course, most of the time, we can guess what they intended to say therefore, our conversations seem to be moving smoothly. However, the reality is one side requires some efforts to others. 

Then, to answer your question about other countries. In my country, Japan, I don't think Japanese don't mind others grammatical mistakes when we talk with them in English since as you may know normally Japanese people don't speak English well. Our level is not high enough to point out others mistakes. We do not deserve it yet. 

And it's not your point but based on my experience of working in the Staets, the pronunciation is more important than grammar when we talk with English natives.