Is possessive's apostrophe dispensable in any case?

There are a few limited cases for which an apostrophe is not used to indicate possession. For example, if you're referring to something belonging to it or her, the correct form is its or hers, with no apostrophe.

Such an exception does not apply to column. If you want to refer to the width of a particular column, you would say the column's width. In the plural case, to refer to the width of specific multiple columns, the apostrophe goes after the "s", so the columns' width would be correct.

However, if you're referring to the width in a general sense, rather than to specific a specific column or columns, then column width would be correct.

Your example quote is incorrect without a modifier such as "the", so it should be:

Is it possible to reset the columns' width to default in the message pane?

... but note that this refers to specific columns that need to be previously introduced in the context. Otherwise, for a general context applying to all columns it should be:

Is it possible to reset column width to default in the message pane?

If you want the possessive form, the apostrophe cannot be omitted. But in the specific case of columns' width, we may just write column width, which is a noun phrase with width modified by column.

For "correct" grammar, you need the apostrophe. Sometimes people forget, don't know, or don't care, which is probably why you'll see (or rather, not see) a lot of missing apostrophes on the net.

Well, it's not always true, a word can be possessive without using an apostrophe.

There was an alien in the UFO. We found its remnants at the crash site.