How can we say these words politely in a business environment? 1. Rude = You are so rude. 2. Stupid = ... 3. Nonsense = ...

Anything can be said in a polite manner

As business between us for each other's  benefit there is no place for rude behaviour between us. 

If any of us show stupdity, it will cause loss to us. 

There is no place for nonesense as our business is for each other's advantages. 

If any of us show laziness it will result in blunder

You are not wrong as long as you agree on this ........

There are several ways and techniques a businessperson can use to soften his/her language and sound polite. Some of these are distancing, using negative or passive sentences, including words that express opinion, using modals...etc. In the cases given I would say:

1. That wasn't polite.

2. It doesn't seem right./I'm afraid that was unprofessional.

3.Apparently that was illogical.

4. Wouldn't it be better if you worked a little harder?

5. With respect, that's not quite correct.

You can not utter these vocalizations in the good humanitarian work environment, which must be based on mutual respect and happiness to others and on the basis of positive thinking at work

To convey your message effectively and yet not sound rude or impolite, these are the polite version of these words:

Rude= Impolite 

Stupid = unsound 

Nonsense = irrelevant 

Along with using the right words, it takes skill in handling and diffusing problematic situations especially if one is in a leadership position. As human beings are unpredictable and emotional entities, tact is one of the main skills that can break down an adverse situation. Passing on a ‘harsh’ message using kindness and gentleness in ones tone can go a long way.

The words rude, stupid, lazy, wrong and nonsense are judgmental and should not be used in a professional environment. However, below are some phrase examples that could be used in appropriate situations.

Rude:  unacceptable, disrespectful, impolite, unkind,

Stupid/wrong: ‘not quite making sense’ or ‘that might not work because…’, ‘let’s try an alternative’

Lazy: ‘Would you mind assisting me with this?’

People can be deemed as ‘lazy’ for many reasons. If they are not ‘pulling their weight’, it’s possible that they are not motivated enough and may need some sort of boost which could require a higher ranking involvement.  They could be directly asked to be involved as they may need that form of personal acknowledgement.  

You can choose to use a formula (not very + the opposite) e.g. not very polite = rude

Or a lighter equivalent with (quite) as an intensifier e.g. rude = quite abusive 

stupid = quite uncomplicated (unintelligent, ill-advised)

nonsense = irrelevant

lazy = inattentive (passive, apathetic)

wrong = incorrect 

I agree with experts answers, thanks for the invitation. 

As language evolves, I sometimes forget the offensive origins of certain words and phrases as my dad help me earlier to exclude from my dictionary! Or Perhaps I never knew them in the first place because my parents learned me not to put others in awkward situation. however, I think that these offensive words began in racist, sexist, or generally distasteful situations.

1-Stupid

I think that , being smart in business means thinking things through or trying to find the real answer, not the first answer. On contrast, being stupid means avoiding thinking by jumping to conclusions. Jumping to a conclusion is like quitting a game which you lose by default.

That’s why Someone saying “I don’t know why sometimes you seems intelligence and other times you look stupid ” oh this judgment because he thought himself smart, and he is refusing to jump to a conclusion.

So when someone says “what is stupidity you're speaking out!” it means he has stopped thinking and say it to feel finished with that subject we discuss, because there’s nothing they can do about that. It’s appealing and satisfying to jump to that conclusion.

So I think that if you decide someone is stupid, it means you’re not thinking, which is not being smart.

Therefore I believe that  smart people don’t think others are stupid.  

2-Rude

Freely, in business it means " it's none of your business! ", you can use similar phrase if you don't like giving away a bit of your private information to somebody who are eager or want to know more about you or even when you have just met . But For me I feel it's somehow rude to say that to someone so directly.

Typically, in various situations in business or people interaction I understand that these people who ask about your personal information  are care about you or  just doing their jobs as customer service or call centers  agents …etc, and you shouldn't to be rude to them.

At the same time, it isn't rude to say a better way please stick into the point without having to ask me about myself.

3- Nonsense

Using that expression as a compliment of sorts, but it's unclear what it means, however, what exactly does "no nonsense" mean when describing a person or a manager?  For me What comes to mind for me I get a picture of someone who is humorless, dour, unforgiving and not very approachable. Someone who would never tolerate anything called "emotional intelligence." Someone "by the book" to a fault. Someone who reminds me of the strict teacher from high school who generated universal enmity.

I apologize for the answer, I leave the answer to experts specialists 

you have to increase your intelligence.

agree with great answers above