Safety of Third party Single Sign-On (SSO) on your network

Hello All,
I have a question about SSO (Single Sign-On).
There is a website that offers a service and in order to use their service they used to require knowing what our IP address was in order to control access to their services by IP. Now they are changing to SSO instead and even though I'm not familiar w/ SSO I know that they would need to connect to our AD for authentication and as we know a lot of breaches happen with Third party companies having access to internal network infrastructure. I don't feel comfortable using this method and since I'm not all that familiar with it I figured I'd ask your opinion. Yes, I do know that NOTHING is 100% secured and full proof but I want to at least make sure that I'm not potentially opening a can of worms.

My questions are:

- What are some of the risks if I chose to give their SSO access to our AD?
-If I decide to go w/ the SSO what are the questions I should be asking them to make sure that they have their "sh#*" together and will not potentially compromise our Server/network.
-What are some of your opinions on going w/ SSO from a Third party vendor?
-Should I implement SSO in this case or hold my ground and ask for another solution?
-Could I use AWS, Azure AD (or similar) to create just a stand alone AD on it's own to use with this service and is is cost prohibitive?

Thanks in advance for all your help, it's greatly appreciated!!