I hope it's not weird. I've been doing that for a long time. IMO, that's in the same category as having an interior door in a different color on either side. I find that I do prefer that the edges be the same color as the exterior or hall color. To be honest, how many people ever notice? It's the sort of thing we pay no attention to until we are nose-to-nose with making a decision, and then we realize we've never really looked at what others do. Unless they are interior decorators or painters, it's probable that the "others" are not going to pay any attention to what we do.

We have cherry woodwork in our library, dining room and staircase and we stained it all the same color. The color came from our kitchen cabinet maker...not that that had to match, but I liked the color on the cabinets so much, I used it in the rest of the house. However our front door is mahogany so we made no attempt to match it, though the stain is about the same tone as on the cherry.

If your stained door is taking a beating from the weather and sun, your painted door will taking a worse beating. So which would your prefer to maintain??

I agree with the Halcyon! It flows with the main house color, but highlights the cedar shake just enough. About the Rainwashed vs Sea Salt- can you get samples painted on the house to compare and see exactly how they look throughout the day? In general it's always best if you can see a paint color on the wall you're planning on using it on, colors look different on a screen vs on a wall with light and shadows, etc.