I’m not sure how much mamzerus is an issue. Doesn’t there have to be a halachic marriage that’s not terminated by halachic divorce? I can’t imagine that’s a common situation.
Also, most children of mixed marriages don’t identify as Conservative or Reform. They most likely are not affiliated, identify as “half Jewish,” and to them it’s at best a cultural identification.
A related question is what percentage of Conservative and Reform “rabbis” are not halachically Jewish.
Joseph brings up the problem of BTs who discover they’re not Jewish. It’s not so hard to resolve — they just need to convert.