Its always going to be tricky. I expect both bands want to make it, do lots of gigs etc and i can totally understand some members getting jumpy about commitment.
Its all very well saying you will honour the first gig in each time (if thats what you have done) but that then leaves the other band with a problem, especially if its originals and they need to get someone in to cover you.
Personally i wouldn't be in a band with someone who was going to cost me loss of earnings, or at least extra hassle. To me its not worth it and un fair.
This is not attacking anyone, and in fact i did it myself for a few years recently but these situations can become messy IMO.
There is no straight answer as none of us can predict whats coming, but in answer to the original post, and in my view of course, if its a new band, with all of you putting in time and effort i dont see why its a problem being questioned on commitment. I would expect both band will want to be first place come gig day.