Not sure how it is on your side of the pond ...
I'm still a relative newbie to the AT world, so my observations may be wide of the mark, and only really reflect my local scene, but I don't see many people from the BR world 'dabbling' with AT, but a few who have taken on tango as an additional family of dance styles, or have made the crossover, leaving BR behind.
There is the category of dancers who are primarily BR social dancers, who attend events where the DJ may play just a handful of AT songs as part of a mixed evening of dancing. Usually, they get up and dance their choreographed routine of pastiche tango they have been taught by a teacher at a dance school, and they seem to genuinely believe that they are dancing tango, when of course, they are not. I was involved, last year, (as demo assistant) in a beginners class at a dance school, that inevitably drew most of its members from that circle, but two by two (they never mixed and wouldn't rotate) they all dropped out, disappointed that we weren't going to teach them what they already knew they wanted. I see some of them, occasionally, at my own social events. I have no objection to them taking whatever pleasure they can from their tango-pastiche, and I too, play a few tango songs. The comical thing is that they dance exactly the same thing, whatever you play.
One or two of them are very good BR dancers BTW, and their technique, including posture, would put many AT dancers to shame, so its not a matter of the standard being attained, but of a mindset.
But back to the issue: I don't find people say they have to leave BR behind, in order to dance AT, and I think the numbers that want to add tango to their repertoire (as I do), or to adopt it as their preferred or sole style to the exclusion of BR, are about evenly balanced. What I do find is that there is little or no support for the transition process, and many people from a BR background receive no useful guidance that would smooth the difficult crossover. They sink or swim. I drowned, myself, and had to start again from scratch, and it was a bruising experience.
An oddity of the groups that I have been associated with is that there are usually three or four salsa dancers and a couple of modern jivers for every BR dancer (who are therefore a tiny minority), but they seem to be readily accepted into the tango world, with none of the negative comment or irrational prejudice that BR dancers seem to attract. If more tango teachers had some solid background in BR technique, they would be far better placed to help beginning tango dancers in the transition to new requirements, but such help is very thin on the ground. Usually, the posture problems that arise result from basic faults in the dancers' BR technique (ie they are bad dancers, or have been badly taught). It isn't that they can't adapt their BR ')(' shaped hold to the top down 'A' shaped embrace: they can't actually do either. They are standing with their weight back over their heels, quite unable to create a viable frame in any style. Their new teachers seem to assume that this is normal, and tell them off for being BR dancers, instead of helping them to stand up properly (possibly for the first time ever) and learn to dance.
Has this got anything to do with this discussion? Yes, sort of.
I have never seen regular BR dancers attend tango events to 'have a go', but where it happpens, I can readily understand the havoc it might cause. Probably the category least likely to attend a tango event casually is the pastiche tango dancer. They would say something like "You mean you dance this style all night?", which for them would mean repeating their 32-bar routine, exclusively with each other, ad nauseam.
I can't see any point in any teacher worrying about losing dancers to other styles (or at least to styles not offered by that teacher). People's interests often change, over time, and if they didn't go through stages in which they favoured a variety of styles, they would probably give up and take up some other hobby. A lot of dancers seem to start with the very unstructured and informal modern jive, and accepting its limitations, as they progress, look for more challenging dances. Anyone providing a narrow range of styles, such as AT, to the exclusion of others just has to accept that there will be a steady flow of people in and out of the style. Arguably, they are competing with fishing and all sorts of other leisure interests, and not just the bogey-man BR salesman. They could offer a wider range of styles, if customer retention was their key goal, and it's their choice to specialise.
ALso, as someone else mentioned, FT ballroom teachers who make their living with classes may also pick up some AT to throw it in their basket
Well I'm dead against anyone pinching a bit of tango (you know: attend a few beginners classes, take the odd lesson/workshop and then launch of the the scene as a 'tango teacher'). I've been accused of doing just that, myself, frequently - usually behind my back, but I take no notice. But I'm all for dance teachers (particularly full-time ones) embracing a wide variety of styles, as long as they do them properly. But the statement I quote here contains an obvious fallacy: recast it as "Full-time dance teachers who make their living ..." would be fine. Excepting high-level coaches in dancesport, I know of no FT ballroom teachers. None. BR is far too small a segment of the dance world to support anyone full time. At the very least, they probably embrace Latin American too, and often R&R, Salsa and proabably Modern Sequence. In my teaching society, new members qualified in freestyle outnumber BR faculty members by 20:1. BR is a very small, niche group of styles (five, of course - all different), and it seems to be in terminal decline, unfortunately.
The very fact that all the range of styles that the typical full-time teacher might offer get rolled into this general term 'BR' (and it is frequently used by tango dancers perjoratively) might be the reason why so few tango teachers can help dancers from other styles in their cross-over issues.
So if a dance teacher starts to offer AT, the tango community should be pleased (assuming some basic competence from the teacher) that someone else is devoting effort to growing the tango dance community. More dancers means more people to attend social events. More dancers means more people looking to attend workshops and special events. More dancers means more business. In a competitive world (and dance teaching can be very competitive, particularly at times, like now, when money is tight), you have to be
good to survive and prosper. Competition is a good thing: it keeps us on our toes.