Maybe it will not have damaging effect. However, it may not help to promote your site when your domain name doesn't have the relevance about what your site is or it doesn't describe the site content well
This is just another opinion
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A domain name with the targeted keywords in it is definitely a positive factor for search engine optimization. As to how important it is, it is left to the search engines to determine
It is just one of hundreds of factors taken into account so you are not dead if your domain name doesn't include your keywords, only that for other things being the same your competitor might rank higher than you. However keep in mind that other things are NEVER the same...
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I like to think of this in terms of opportunity cost: That is, by using a domain name that is NOT intuitively related to your site, you're not directly losing something that you had, but you ARE passing up on an opportunity, namely, the synergy / value / potential SEO upside of having a related domain.