Ha ha, I know what you mean about the accents.
I do work with children - mostly with dyslexia - but for many, that involves difficulties hearing or making the sounds as well (plus a variety of other language problems), so I spend time getting them to look at how they make the sound, trying to feel it, etc.
the f/th thing is compounded by the fact that there are many regional accents where they pronounce them all as F, so it's not necessarily 'incorrect' - but it's not standard English, and can make spelling more difficult if they can't hear the difference, so I do still try to get them to say the words correctly for that purpose. They can of course decide whether they want to say them in a standard way or not depending on their environment.
It is very difficult to change once the words are learned, however. Someone who really wants to can, but it takes effort, like breaking a habit. For someone who knows how the words are spelled, then they can use that as a way of knowing how they should be saying the word, and train themselves to do so. For a dyslexic child who doesn't know how the word is spelled, that isn't very much help! I have some who try so hard to get them right, and then over correct, so count, for example, one two free thor thive.
It's a difficult sound in many languages, and there are interesting differences in what sounds people use to replace 'th'. Sometimes it's 't', sometimes 'z' (for the voiced one), sometimes 'd'. The point I was making about how people replace th sounds with either f or v, even when they say that they can't hear the difference between the two 'th' sounds, is that their brain clearly is distinguishing between them and replacing them with another sound with the correct voicing. They just aren't consciously able to identify that.
A lot of accent is the vowel sounds, sometimes the stress position, sometimes consonants, and there are sometimes changes in syntax and vocabulary as well that characterise a particular dialect/region. And all of those transfer to a second language as well - sometimes in distinctive ways. People vary in their ability to hear the differences between sounds and to copy accents, and it does get harder as you get older.