I don't think MeryFlyer and Baobab will mind. I only had one OMNI-hotel experience some years ago: In New York / Manhattan (this OMNI has changed ownership since than): I had a reservation (3 nights, booked through my travel-agent) and wasn't an experienced traveller as now. Arriving late from Europe, they did not accept (find) my reservation and declared to be full (I did not have my reservation number handy and there wasn't any such number on my hotel-voucher - and it was to late/to early to call my travel agent back in Europe right away). I finally had to go (for one night) to a horrible Howard Jonson (9 Ave?) till my travel agent fixed things the next day (and I had to say thank you for an excuse of the OMNI-manager and one free breakfast overed by the OMNI; my travel agent at least paid for the taxi-transfer, the phone-calls and the first night). WHY WASN'T THIS BOARD BORN BEFORE!
So - in my (very limited and egoistic) opinion, nobody will mind if their "hated" airline has an alliance with OMNI-hotels.