None of the Splitcoaststampers daily challenges are vendor specific. You can find a list of them here:
Splitcoast Challenges Forums: Daily Challenges Throughout the Week
Although Stampin' Up colors are used for reference in the Color Challenges, SU products are
not required.
You can also find a slew of challenge blogs on this site:
Paper Playful
Some of them may be linked to certain companies, but many are not.
None of the challenge blogs linked in my signature are specific to any company, either.
52 {Christmas} Card Throwdown is a fun way to get started on your holiday cards.
CAS - Colours and Sketches alternates color challenges and sketch challenges to create clean and simple styled cards. Both of those are weekly challenges.
Cards in Envy presents a new challenge every two weeks; these are theme challenges, but the "in Envy" part of the challenge means that your card must be A2 sized with no lumpy bumpy embellishments, so that it can be mailed in a standard envelope with no additional postage.
I hope you'll find something to your liking!