I can't claim to be an expert in SEO but I don't see much downside for your homepage. Any external links to now point to http://website.com/forums will still work, though they will direct people to the forums feed rather than the homepage. l still think that all of the "link-juice" should still be okay though you may have a weird situation where your forums rank higher than your home page.
There could be a bigger problem though if this changes all of the urls to posts, articles etc depending on your current url structure. For eg if you have an external link to http://website.com/forums/forums/topic/thisisthepost and you then lose that middle /forums/forums from the url without a redirect, the link will show up as broken and you won't get any SEO benefit from it. If you are able to keep existing urls or redirect them, then you should be fine.
Anyhow, that's my non-expert 2c worth.