As it has been said so many times, tech privacy aware people are the minority. It won't make any difference for my non-tech neighbor (in fact, he will probably be delighted if it helps him with something).
Unless there is a specific, believable, near term risk people will just ignore it.
Most would submit genetic material to 23andme and similar organizations with no restriction on its use. Yes, if could theoretically backfire not just on them, but also on their kids. But unless they see it as a near-term likelihood they will not care enough. My 2c.