Multiple ids should be used in the reRender attribute to Rerender multiple sections in VisualForce page.

Sample Code:

Visualforce page:

<apex:page controller="SampleVisualforcePageController">
    <apex:form >
        <apex:pageblock >
            <apex:pageblockSection id="membersBlock" title="Member Details" >
                <apex:pageBlockTable value="{!listMembers}" var="member">
                    <apex:column value="{!member.Name}"/>
                </apex:pageBlockTable>
            </apex:pageblockSection>
            <apex:pageblockSection id="accountsBlock" title="Account Details" >
                <apex:pageBlockTable value="{!listAccounts}" var="account">
                    <apex:column value="{!account.Name}"/>
                </apex:pageBlockTable>       
            </apex:pageblockSection>     
            <apex:pageBlockButtons location="bottom" >
                <apex:commandButton value="Fetch" 
                    reRender="membersBlock,accountsBlock" 
                    action="{!fetchRecords}"
                />
            </apex:pageBlockButtons> 
        </apex:pageblock>
    </apex:form>
</apex:page>

Apex Controller:

public class SampleVisualforcePageController {
   
    public List < Member__c > listMembers { get; set; }
    public List < Account > listAccounts { get; set; }   
   
    public void fetchRecords() {
        
        listMembers = [
            SELECT Name 
            FROM Member__c
            LIMIT 10
        ];
        listAccounts = [
            SELECT Name 
            FROM Account
            LIMIT 10
        ];     
        
    }     
    
}

Output:

Before clicking “Fetch” button:

After clicking “Fetch” button: