Part of the BLW theory is that a baby's system *should* be mature enough to handle most foods after 6mos. Of course lots of moms will tell you their LO's had sensitive tummies much longer than this. Personally I always felt that after 6/7mos with my LOs, anything goes really. BUT if you are worried, you could start cutting back on the amounts of different foods you are offering and seeing if it makes a difference. Some foods too are more likely to cause trouble than others, like grains or dairy, so I'd cut those out first. But I think in general most fruits and veg are just fine unless baby has a sensitive tummy.
Again IMO, it's totally not true that offering finger foods now will mean baby will not be able to use a spoon. In fact you can start giving a preloaded spoon now and letting baby learn how to use it. I actually think if anything the opposite would be true, and that a BLW baby would learn how to use cutlery sooner because they have been practicing the motor skills needed by feeding themselves, where as a spoon fed baby doesn't get to use their hands at all, kwim? I think I would take your mother's opinions into consideration, and politely acknowledge them, but trust your instincts.
Also, even a spoon fed baby will make a mess with food once they start getting finger foods, whether it's at 7mos or a 1yr, so I think if you start earlier then they get the hang of eating earlier and the mess becomes less earlier, kwim?