Let's ask Google.
"democratic senators"
> About 969,000 results (0.52 seconds)
"democrat senators"
> About 92,800 results (0.42 seconds)
Bonus: "democratic senators" site:breitbart.com
> About 1,010 results (0.32 seconds)
"democrat senators" site:breitbart.com
> About 2,300 results (0.27 seconds)
Conclusion: "democratic" is significantly more common outside of right-wing propaganda.
By analogy, you'll more often hear "Texas senator Mr Bean" (using the singular noun) vs "Texan senator Mr Bean" (using the adjective).
In any case, it's not something anyone should get worked up over.