Your job is not to build the perfect/best product, it's to build the one your client want and is willing to pay money for.
If you tell the client that they're wrong and that you should fix the critical bug first how they react is a really good test of whether or not they're going to be a good client. If they insist on fixing the lower priority bug first then you should try to stop working with them, because at some point in the future they're going to demand more unreasonable and stupid things that blow up in their face, and you'll lose that client anyway. Save yourself the stress of working with bad clients and get rid of them at the earliest possible opportunity.
If they accept that you know what you're talking about and give you agency to fix things in the order that you think they should be fixed, do your absolute best to keep that client happy because they'll be a joy to collaborate with for years.
> If they insist on fixing the lower priority bug first then you should try to stop working with them
I'm all for firing bad clients. Fire the crazy ones. Fire the ones that don't pay. Fire the ones who make ridiculous demands at the last moment.
But the client wants you to deploy a fix to the logo ASAP, you do it. That's the client's priority. As long as they accept the disruption to the rest of the work, it's no problem.
If you tell the client that they're wrong and that you should fix the critical bug first how they react is a really good test of whether or not they're going to be a good client. If they insist on fixing the lower priority bug first then you should try to stop working with them, because at some point in the future they're going to demand more unreasonable and stupid things that blow up in their face, and you'll lose that client anyway. Save yourself the stress of working with bad clients and get rid of them at the earliest possible opportunity.
If they accept that you know what you're talking about and give you agency to fix things in the order that you think they should be fixed, do your absolute best to keep that client happy because they'll be a joy to collaborate with for years.