Can you replace may be with shall be or will be?

it may be cold tomorrow  =  possibly

it shall be cold tomorrow =  probably  (it has been decreed by someone)

it will be cold tomorrow =  definitely

so...... no, you can't

“Shall” is usually confused with “will” while the usage of “may” is often interchanged with “can.”. Both “shall” and “may” can be used as part of the question. In the same manner, both words can be included in the answer with “shall” or “may” in the question.

All are modal auxiliaries but there are apparent differences.

"May be" implies permission, possibility,wishes, purpose, concession , "shall be" reflects futurity, willingness/intention, suggestion and finally "will be" implies willingness, intention, prediction, insistence,requests in questions.

You can in some instances. But you change the sense:

It may be sunny tomorrow. It will be sunny tomorrow

One is a possibility, another something of a certainty.

If one offers professional advice for a living, may will

be the better choice.

Using "may" be vs "will" or "shall" be isn't the same meaning! For example, "You 𝙢𝙖𝙮 be the winner" doesn't say you are or will become the winner. But changing it to "You 𝙬𝙞𝙡𝙡 be the winner" says you will become the winner in the future. So the first one is merely the possibility of your winning. The second is your definitely becoming the winner, big difference!

I agree with your correspondent 'Bill'. 

However, I wold add that 'shall ' refers to the first person, and 'will' refers to the second person. . 

e/g/ 

'I shall be at the station. 

& 

'You will be at the station'. 

maybe, maybe not

That changes the meaning, but if a sentence had "may be," chances are it will still be grammatically correct if you substitute "shall be" or "will be."

The bandanas may be green.  (Green is allowed.  Or, I'm taking a guess that they might be green.)

The bandanas shall be green.  (This is a directive specifiying that they must be green.)

The bandanas will be green.  (Just stating a fact.)

no

 shall and will are definitive  action verbs and maybe is not definitive