Does my parents buying a home affect my financial aid (FAFSA)?

Is this going to be their only home and their personal residence?

The money that they put down as a deposit would have been an asset either way - as cash in an account or as part of the home cost. The school may treat those assets differently (cash vs. home ownership) but it will depend on the school. And as @Madison85 alluded to, a first home generally gets a free pass (certainly for FAFSA).

For a FAFSA only school…you primary residence is NOT factored into the formula…at all.

If they bought a second or vacation home…the equity in that would be considered an asset on the FAFSA.