The first thing I would ask is how you define "legitimate"?
If these "legitimate" sites are websites for actual businesses in your industry then the answer to your question is no. It is not a bad idea to get a bunch of links from legitimate websites that have low Moz scores.
Moz scores only reveal certain aspects of what makes a good linking site. One aspect moz metrics do not measure is relevance. A relevant site in your industry with low Moz metrics linking to your site can possibly do more benefit to your website for SEO purposes than a non-relevant site, unrelated to your industry, with high Moz metrics.
Another consideration to take into account is a site may have low Moz metrics this year but grow to have high Moz metrics in future years. For most realtor websites that are new as you have mentioned, this is likely going to be the case. Getting a link on the site will grow in benefit as the site gains authority and trust with time. Therefore, there is nothing wrong with getting a suitable link on a site with low Moz metrics and there could be great upside future rewards.
The potential problem I'm seeing with your strategy though is that there is a strong possibility that the sites that put a link up to your site for the free program will not keep the link on the site for the long-term, especially when the link doesn't make sense on the site and possibly look spammy. Considerations to have the link applied with suitable contextual text that make sense for the linking site will both be more fitting for them and also beneficial for the SEO of your site.