Much will depend how you structure these new links.
I'd recommend every users' site is either
Operated as an individual site - ie, no links from your site to the users' sites - and you link each members' site back to your home page.
This has the effect of each members' site looking like a link into your site. The off topic links will then have little effect. In other words, try not to link to the individual members' pages, unless they are on topic.
I'd think the majority will be, as you say, dog-releated, so the benefits should outweigh the potential downside.
If you have to treat the members' sites as part of your own site (Linked from a page on your own site), then ensure you place your own, on-topic links in prominent positions from the members' sites.
It's inbound links that do all the good for you, with outbound links doing less harm than you might imagine - especially as in 1 above.