All of them (putain, bordel, merde) are clearly rude words, and are far from being considered acceptable in all situations, or as words from a standard register. For instance, none of these would be acceptable in a job interview. A secondary school teacher teaching in the presence of another adult (another teacher, inspector, parent...) would certainly avoid using any of them. Nobody would use them in writing in a normal professional context.
However, they are all extremely common in colloquial French, in conversations with friends, in self-directed speech (« Merde, j'ai laissé tombé mes papiers »), and are frequently used in informal conversations with colleagues for instance.
The question of their acceptability highly depends on the social context: who is talking to whom (social origins, age, socio-economic status, power relationship...), where and for what.
In a professional context, outside of informal “coffee-machine” talk, their use is clearly possible, but would probably occur in an angry or highly emotional reaction. I could typically imagine Emmanuel Macron use any of the three in a harsh internal discussion with his ministers (actually, Macron has used bordel in a public conversation with another politician, but in its substantive form — « foutre le bordel » —, and it caused a small scandal; another example: Sarkozy used merde in a private phone call to the president of his party). In school too, I remember one or two teachers flying off the handle and using merde and bordel (not putain, but that was a long time ago; it could certainly happen today, depending on the formality of the school).
In general, I think merde can be considered milder than bordel, itself maybe slightly milder than putain: merde < bordel ≤ putain. If you are familiar with their equivalent in English, I believe merde is used with approximately the same level of informality as shit, and putain corresponds very closely to the uses of fuck.
Regarding regional differences, in France, they are more frequent and considered milder in the South of France than in the North. Generally, the North (Lille, Nancy...), as well as Belgium (and probably other peripheral regions such as Switzerland), tends to be more conservative and these words are there less acceptable than in Southern France, where they might be ubiquitous.
(EDIT: I corrected the last paragraph regarding regional differences. Previous version was: “I am not aware of strong regional differences on the matter. It is probably less frequent in Belgium (as possibly in Switzerland) than in France, and more common in the South of France than in the North, but I am not even sure the difference is significant.”)