I think I have a Malaysian accent but Malaysians think I have what they perceive as a desirable accent and foreigners ask (or aks, lol) how is it that they can understand me better than other speakers of English (regardless of NES or NNES)? Americans think I have a British accent and British think I have an American. (I doth protest and I think I have neither. I have a Chinese accent and I use colloquial expressions that signal my Malaysian-ness.)
There was this time when I worked at a home-stay and we had a Russian, Finn, an educated couple from London, a less educated man from London, an Australian, Dutch, French, an immigrant naturalized American citizen of South Asian descent, an Indian, Thai, Italian, Ghanaian and Iranian all seated for brunch and chatting. As conversation got more complex, I had to interpret English between two people who were speaking English. At one point, the Russian asked how is it possible that she can understand a Malaysian speaking English better than she could an NES Cockney accent? The "lost in translation" episodes were not limited between the Russian and the Cockney accent.
Having had many of these situations happen throughout my life, it makes me err on the side of NES with the caveat that they must have at least a Bachelor's or are aware of carrying themselves, culturally, as middle class. When accents deviate too far from what pop / media culture presents (I cannot understand Russell Brand, actually), it sort of renders all English language capacity null and void.
The only thing I can't stand about Filipino accents is the way they fake the American accent. I had a Pinoy boyfriend who grew up in the US and he had a beautiful Filipino American blend that's as sexy as a South American accent. I also had a Manila wannabe Mestizo boyfriend who was upper middle class and he makes me want to throw up when he puts on his accent.... Which goes away when I get him mad enough to launch into a tirade when we fight. Like how to stay mad in an argument when someone has that accent, really.
What's undesirable about the Filipino accent is how nasal it sounds but it's not across the board. Filipinos must agree with us on this in order to spin an entire cottage industry providing training for people to sound like what they're not. I'm not sure whether it's Ilokano or those from Cebu where the accent isn't so undesirable.
I wouldn't know what I would do if I had an undesirable accent. Would I get training and fake it? That's not the most authentic way to live. But I'd definitely not teach English to anyone who isn't my own ethnicity and compete for legitimacy just so I can make a lucrative living elsewhere. As it is, I only teach English locally to my own people and to Japanese, Koreans, Chinese, Thai who come to Malaysia and seek local teachers.