SO today I saw Yoast SEO was “Grey” coloured when I opened my homepage. So should I start doing SEO of the homepage or let google pickup latest post as the meta-description of my website?
Yoast showing Red, Green or Grey does not says much about the SEO of your homepage frankly. Those indicators are just based on a few on-page SEO factors like title size, meta description size, keyword density and related stuff.
There are sometimes when you cannot actually do ( or you not need to ) do anything much for the homepage, but its really dependent on the type of website.
Someone managing a local business site like me needs to put a lot of work on SEO of homepage since the homepage attracts a lot of traffic.
Someone managing a blog site (For e.g Say a site with technical tutorials or guides ) need not to work much on the SEO of homepage, since its articles that attract most traffic from search engines.
There can be many more points that we can involve here while discussing SEO if we know more about your site.
Otherwise, sometimes ( or I say most of the times ) its best to ignore all these metrics shown by different tools and just work on content quality and user experience.