Also, remember that almost everything in a "bid" or contract is negotiable so you can go under contract with an inspection contingency and have the ability to back out if unsatisfactory.

Why might the sellers ask for this contingency and has anyone been able to void on HOA? 

All cash, close quickly, zero contingencies other than clear title which is how I've operated the past 10 years or so. 

Hopefully you have contingencies to handle a subject to appraisal.As @Jonathon Taylor indicated, in many/most markets the value of an ADU (as set by appraisal and/or selling) is less than the hands off ADU addition cost. 

don't run out of money and have contingency plans for everything.

There is specific verbiage HUD requires in the purchase contract to protect the borrower and disclose some of the 203k contingencies to the seller.

Because appraisals are non-refundable, they are completed after all contingencies (such as a home inspection) have been met and are usually one of the last steps completed before the purchase is complete.

But, as to making an offer, you can add a home refinance contingency to the offer stating that the offer is contingent to you refinancing your home at a certain rate by a given date.Along with the refinance contingency, be sure to add home inspection, appraisal, and financing contingencies.

Are there any recommendations to provide some contingencies that I could look into?

Caprate is coming to barely 5% (somewhere around 4.9) with 25% down (inspection contingency likely but we are not sure in this market).