If we are gifted a property via an irrevocable trust, and sell it for the amount it appraised at when the trust was created, do we need to include it in our taxes?

Yes you must report the sale no matter what the bottom line is since the IRS got a copy of the 1099-S for that you did at closing. 

You need to ask the attorney who drafted the trust or a CPA or enrolled agent who is VERY knowledgeable about irrevocable trusts. 

Many irrevocable trusts are designed so that the grantors of the trust will include income on their own 1040s rather than report on the trust's 1041 return. Usually this results in less tax because trust tax brackets are compressed (e.g. higher tax at lower $).  [This results in you paying tax on income you never receive, which is super effective in making further gifts while avoiding gift tax.] However, many irrevocable trusts must file their own 1041s.

Also the appraisal is not usually relevant for income tax. What matters is the basis you had in the property when it was transferred to the trust. The basis of the gifted property in the hands of the receipient is the donor's basis.  [Unless the donor dies and you inherited the property, then there is a step up  in basis to the fair-market value.] You report your sale proceeds - basis. I am not sure if the trust can tax the section 121 exclusion if you resided in the property, but I'm dubious about that.

The appraisal is, however, super relevant to the gift tax return (Form 706) that you had to file in the year you transferred the property.

Again this is a very complicated area and you really need the help of a professional who knows this stuff.

Doesn't matter if you get an information return or not. Have to report all income unless there is a reg or other guidance saying not to.

The issue here isn't so much as to whether or not to report, but who has to report. The trustee or the grantors.