The answer is maybe. It all depends on your loan. Most banks are waiving the requirement to have the tax transcripts in hand to close a loan as long as they have a signed 4506-T form. So even though The IRS tax transcripts are required by the banks, they are going to let these go ahead if the have the signed form, so they can pull those transcripts when the government is back from this little vacation of theirs.
While some of the areas of the government that affect government backed home loans don't get their money through appropriations, and are not affect by the shu down, some areas are. So if you have or the person buying your home has a government backed loan, you will probably experience a delay.
Of course all this uncertainty affects the market. The market has slowed a bit more than normal heading into fall. So everyone keep your fingers crossed, and hope out leaders get bacck on track.