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If you refuse to sell the house, then in a worst case scenario the buyer could sue you for breach of contract
, and seek "specific performance" (i.e., a court order requiring you to sell the house). Although you can discriminate against sex offenders when opting who to sell to, you cannot breach the contract once it's been signed. Accordingly, if you prefer not to sell to a sex offender, then that is an investigation to conduct before signing the contract. So, if this were to end up in court, I think that you'd lose.
Of course, the above is just one outcome. In a best case scenario, the buyer would just walk away and not sue.
You may wish to subtly mention to the buyer's agent that you've had second thoughts about selling and see his reaction. For all you know, the buyer has had a change of heart as well and would welcome the opportunity to cancel the sale and get a refund of his earnest money. But if push comes to shove, and the buyer is steadfast, then I believe that you'll have to sell.
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