Is OpenDNS safe to use?

In my opinion, it's perfectly fine to use, and probably a very good option for a home user. Perhaps you should elaborate on your specific concerns?

I think it's OK because it seems well resourced (due to its business success), and has otherwise signaled "good" intentions. By virtue of its size, it is well placed to protect against malicious websites.

From Wikipedia:

OpenDNS is a company and service which extends the Domain Name System (DNS) by adding features such as misspelling correction, phishing protection, and optional content filtering. It provides an ad-supported service "showing relevant ads when we [show] search results" and a paid advertisement-free service.

The company’s Umbrella cloud-delivered security service secures enterprise users from malware, botnets and phishing on PCs, laptops, and tablets. The OpenDNS Global Network processes ~50 billion DNS queries daily from 50 million active users connected to the service through 20 data centers worldwide.

This does mean that you have to trust OpenDNS not to do bad things - because they will see all your DNS requests, they can tell what websites you're visiting. Again, signals of good intent will factor into your decision about whether or not to trust them.

Many other companies offer similar DNS services: Almost any major antivirus vendor will have it built into their product, plus there are companies targeting businesses with dedicated appliances that do the same thing.

OpenDNS is a good service for home use to block unwanted contents, but as far as privacy is concerned, yes you are sharing all your URLs with openDNS.
But openDNS ensures that your request is safely reached at their servers without interaction DNScrypt .

By using appliance your privacy concerns could be safe but you need some technical expertise to configure these appliance, because it will be installed at your home. If you have enough technical expertise you can use free tools like Untangle.