If you sold your primary personal residence and you lived in and owned the home for at least two years in the five year period on the date of sale, you do not have to report the sale if your gains are less then the exclusion amounts of $250,000 if filing Single or $500,000 if filing Married Filing Jointly (and both lived in the home for two years).

If you had a gain greater then the exclusion amounts then you would have to report the sale.

Also, if you received a Form 1099-S for the sale, either with a gain or a loss, the sale has to be reported although the gain would not be reported on your form 1040 and you would owe no tax if your gains were under the exclusion amounts.

If the gains are excluded it will not affect your tax bracket  however if you cannot exclude it the cap gains will increase your AGI and can elevate your tax bracket ... nothing you can do to stop that and the cap gain may not be at a zero % any longer. 

You will NOT be pushed into a higher tax bracket.  The capital gain on a  qualified home  sale, is "excluded" from your tax return. That is, it never shows up on form 1040 and does not become part of your adjusted gross income (AGI) or taxable income. Usually you exclude it by not entering it anywhere on the tax forms**.  But, if you get a form 1099-S (check your closing papers), you report the sale on form 8949. The taxable  capital gain amount will be zero. 

So, technically it's not that you have zero capital gains tax; it's that you have zero reportable income. So, zero added to your other income does not push you into a higher bracket.

**Even though it doesn't get reported on the tax forms, you do want to enter it in TurboTax (TT), so that TT can prepare the exclusion worksheet for your records.