I have a Noggin subscription that I pay for directly to Noggin, and am logged in through my Noggin app.
When I try to watch a show that is through "Noggin on the Roku App" it only allows me the option to start a 30 days subscription trial, then pay for Noggin through the Roku channel. Is there a way to log into my Noggin account through the Roku Channel App?
(The email addresses I use to log into Noggin and Roku are different)
No, to log in through The Roku Channel you would have to have subscribed through Roku, not directly with Noggin.
To access it on Roku install and use Noggin's own dedicated Roku app:
https://channelstore.roku.com/search/noggin