java.util date-time classes are outdated and error-prone and so is their formatting API, SimpleDateFormat. I suggest you should stop using them completely and switch to the modern date-time API.
If you are doing it for your Android project and your Android API level is still not compliant with Java-8, check Java 8+ APIs available through desugaring and How to use ThreeTenABP in Android Project.
Learn more about the modern date-time API at Trail: Date Time.
Using the modern date-time API:
import java.time.OffsetDateTime;
import java.time.format.DateTimeFormatter;
import java.util.Locale;
public class Main {
    public static void main(String[] args) {
        System.out.println(formatDateStr("2020-09-23T13:45:13.371Z"));
    }
    static String formatDateStr(String strDate) {
        return OffsetDateTime.parse(strDate).format(DateTimeFormatter.ofPattern("EEEE, MMMM d, uuuu", Locale.ENGLISH));
    }
}
Output:
Wednesday, September 23, 2020
Using the legacy API:
Note that Z in the date-time stands for Zulu time (0-hour offset) and therefore make sure to set the time-zone to UTC.
import java.text.DateFormat;
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.util.Locale;
import java.util.TimeZone;
public class Main {
    public static void main(String[] args) throws ParseException {
        System.out.println(formatDateStr("2020-09-23T13:45:13.371Z"));
    }
    static String formatDateStr(String strDate) throws ParseException {
        DateFormat inputFormatter = new SimpleDateFormat("yyyy-MM-dd'T'HH:mm:ss.SSS'Z'");
        inputFormatter.setTimeZone(TimeZone.getTimeZone("UTC"));
        DateFormat outputFormatter = new SimpleDateFormat("EEEE, MMMM d, yyyy", Locale.ENGLISH);
        return outputFormatter.format(inputFormatter.parse(strDate));
    }
}
Output:
Wednesday, September 23, 2020