There is not a federal tax benefit for contributing to a 529 plan - the benefit of contributing to a 529 plan is that any earnings generated are tax free if the funds are used for qualifying educational purposes.
With that being said, some states do have deductions on the state income tax return for contributions made to their state's 529 plan. I am not sure what state your parents are residents of - but you mentioned Virginia, so I am thinking your parents may reside in Virginia. if that's the case, Virginia 529 account holders who are Virginia taxpayers may deduct contributions up to $4,000 per account per year, with an unlimited carryforward to future tax years, subject to certain restrictions. Note the beneficiary does NOT have to be a Virginia resident, nor does the beneficiary have to attend a college in Virginia.
As for if their contributions would impact FAFSA, I cannot comment on that as it is not an income tax question. I would recommend contacting the financial aid office of the college to ask that question.
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