If a person has a rental property in the UK but lives and is resident in Poland, is that person still allowed a tax-free personal allowance?

Because Poland is a member of the European Economic Area (EEA), a national of Poland is entitled to a UK personal allowance (currently £8,105) against their UK source income, just like a UK citizen is entitled. I would advise you to register for the non-resident landlord scheme, so that you can receive your UK rental income from the tenant (or UK agent) without the deduction at source of UK income tax. If your total UK income is less than the UK personal allowance it is probably not worth completing a UK self-assessment tax return, since you have no liability to UK tax.