What project should be done first paint house interior or refinish hardwood floors?

It isn't so much the dust that could/would ruin the paint finish, but the act of washing a not fully cured (not just dried but fully cured - laytex or water based paints can take 30 or more days to fully cure) which could damage the paint finish.

Also, the floor finishers can damage the walls during their sanding activities.

Best bet is to wash well, rinse, then prime your walls first (making a nice washable surface). Then invite the floor re-finishers in.

Next clean up well after the floor is refinished (and waiting until the recommended time regarding the floor finish being FULLY cured). Then have the floors fully protected, dust off/ bite sand if necessary, dust again then re-wash and rinse the primed walls, make any patch/repairs necessary, prime those patched/repaired zones, bite sand the newly primed areas, then paint away.

No matter how careful the floor sanding folks are - there is almost always a ding or nick somewhere - if you are lucky enough to not need to do even a minor scratch repair count yourself lucky. However, if you understand the likelyhood of it happening and plan for a few repairs - you won't be upset, and won't have wasted your time and efforts on a finished paint job pre-maturely.

flooring should be done last prior to paint touchups, finish trim carpentry, and pre-turnover cleaning.

this is so they are not damaged by any other work.

if you take adequate preventative measure to ensure they are not damaged (by covering them properly), they can be done at any time in the construction process so long as the hvac (if applicable) is running so the internal climate (humidity and temp) are the average that the hardwood flooring will be experiencing during its lifecycle (wood is hygroscopic in nature).

What Eli says is true about the machines they use can ding up base, so its often best to install the base after the wood or remove it and reinstall it if its already installed. If minor touchups arent a problem, then it isnt an issue.

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The right way and the wrong way.

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