It was so interesting I just couldn't stop.
Since I can't post my comments there, I will answer the question here, then.
I used to sound non-rhotic, but now I'm more rhotic. I'm a Japanese person teaching English in Taiwan. My original accent was non-rhotic, because Japanese English is essentially non-rhotic, and I was taught British English. Most of my friends when I lived in northeastern England were from Singapore, Malaysia and Hong Kong, all of whom were non-rhotic (unless they were faking an American accent or something).
But I went rhotic after I came to Taiwan. There are several reasons to that. First, in Taiwan, rhotic seems to be the prestige accent. I once saw a book that taught KK音標, and it said you should pronounce the rolled /r/ because it will make you sound more 溜. (Actually, this is one of the reasons why many non-rhotic foreigners think Taiwanese people sound caricature American.) People thought my accent was 不標準 when they heard my non-rhotic English and concluded it was because I was Japanese, not because I was trying to sound British. Third, Jennifer Jenkins said rhotic was more intelligible in lingua franca communication. I guess that's true, because we Asians generally learn how to spell English words before we learn how to pronounce them. It seems more "logical" to me to insert an r sound when there is an r in spelling. And in RP, there is the inconsistency of having to pronounce the r when the next word starts with a vowel. Lastly, I lived in the Philippines for almost three years and have lots of Filipino friends. In the Philippines, people, especially those with lower English proficiency, have difficulty understanding you if you sound non-rhotic, perhaps because you sound so different from the way they are taught what English words sound like.
I do sound a lot more non-native when I sound rhotic (maybe because it was in the Philippines that I learned to sound rhotic), but my students seem to understand me much better when I sound rhotic. This is probably because they're familiar with what I call the "KK音標-inspired accent". And it doesn't matter if I sound non-native, not least because they thought I sounded non-native even back when I was trying to sound as British as possible in class, probably because of my Asian face and Japanese surname. (Besides, we all know that native speakers are only a minority of English speakers.)
I have noticed, though, I subconsciously switch back to non-rhotic in several situations. First, when I'm having very relaxed conversations with, say, my wife, I turn non-rhotic, because that's my original accent in the first place. I also turn non-rhotic when I have to "impress" someone with my "high class" British accent, especially when I have to talk to a teacher who, I feel, looks down on me because of my non-nativeness. (Isn't this the use of Bourdieu's "linguistic asset"?) Also, I tend to suddenly turn non-rhotic when talking to a non-rhotic interlocutor, for example, a Briton, perhaps as accommodation strategy. I sometimes notice that I’m speaking non-rhotic when conversing with other rhotic native speakers or fluent L2 speakers, probably because I know that they have high proficiency and subconsciously think that they shouldn’t have any problem deciphering me.
Consequently, the best place to hear me sounding rhotic is classrooms.
The dilemma is: I sound rhotic because I think students can understand me more easily; but students may think my English is limited because I sound more non-native when I’m rhotic.
One solution would be for me to pick up a native-like American accent. But I really can’t imagine myself doing that. I used to dislike my classmates who had an American accent and used to label them as fake Americans. And I don’t want to be a target of a terrorist attack when visiting some Islamic countries.
