The connotation that goes along with "come out" is a bit finer than just saying that you disagree or agree with something. It is more as "take a stance" on something. The difference here is that you can only really "take a stance" once - the first time you make your opinion clearly known.
To make this clearer, let me give you an example. When President Obama gives his speeches, he is not "coming out" for or against each issue that he talks about every time he talks about it. When he recently gave a speech applauding the Supreme Court's decision legalizing gay marriage, it wouldn't be right to say that he "came out" in support of gay marriage, because he has been supporting it for the last 4 years.
However, the first time that President Obama spoke on this issue and took a position, it would be correct to say that he "came out" in support of gay marriage.
Now, back to your question:
I'm at the meeting where we discussing some techincal topics and I
want to disagree with a way my colleague proposed publicly. Can I say
I would come out against it.
Is that grammatically correct?
Because you'll making your opinion publicly know clearly for the first time, it is fine to say that you would come out against it.