According to the CDC chlorinated pools are okay.
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There is no evidence that COVID-19 can be spread to humans through the use of pools, hot tubs or spas, or water playgrounds. Proper operation, maintenance, and disinfection (e.g., with chlorine and bromine) of pools, hot tubs or spas, and water playgrounds should inactivate the virus that causes COVID-19.
“While there is ongoing community spread of COVID-19, there should be appropriate care taken both in and outside the pool, to protect yourself and others. Owners and operators of community pools, hot tubs, or spas should follow the interim guidance for businesses and employers to plan and respond to COVID-The World Health Organisation recommended chlorination level of 15mg.min/litre is sufficient to kill non-enveloped viruses such as poliovirus, rotavirus and coxsackievirus, and an enveloped virus such as Covid-19 would be inactivated at even lower levels, the document says.”