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I always remove the tub before tiling myself. Same goes for sink and loo and pipes and whatever.
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I was taught that Silicon is not good under compression, it was designed to stretch. As such I never fill baths prior to Silicon, the stretching abilities of Silicon should be sufficient to accomodate movement of a millimetre or two easily. If a bath moves more than that I think there are other issues to address and whether the bath was full or not I don't think it would make a lot of difference.
swe !! most baths require the tile to finish on top of the bath , so it is required to be in situ , unless it is a stand alone.I always remove the tub before tiling myself. Same goes for sink and loo and pipes and whatever.
it makes sense swe to make bath panels removable, its very popular here to frame baths and tile over leaving no access..