Socialism does not mean expecting everyone to have equal wealth, only that those who are wealthier pay more towards the common good than those who are not.
If you accept that even a socialist has a right to use their skills and talents to accrue wealth then you have to accept that it is ok to be a wealthy socialist, so long as none of that wealth was accrued by dodging taxes.
A socialist might well want to vote for a party that would increase taxes and make all schools well resourced but the truth is that such a party has not yet managed to be elected and retain power sufficiently long to fix the state education system.
That being the case, a socialist could choose to give all their wealth to a charity that strives to improve education outcomes for as many as possible, and send their child to an inadequate state school on principle, or they might spend the money on buying a home in the catchment of a less-inadequate state school, or they might just spend their money on other luxuries, or they might spend their money on upgrading the educational experience of their children beyond what the average taxpayer is willing to fund for the state sector.
I honestly can't see a moral imperative why any of these options should be chosen or rejected. They all seem valid to me. No one wealthy kid going to a comp is going to have a beneficial effect on anyone else's outcomes. Actually funding state schools adequately would take a massive cultural shift in the levels of tax the country is willing to vote in favour of and if you can't see the socialist revolution happening before your child reaches the age for schooling decisions then you have to base your choice on the real world not some imaginary utopia.
I do wonder whether those asking questions like the OP maybe can't get their head around the idea that one human might simultaneously be empathic enough to their fellow humans to believe in socialist principles and also clever we enough and talented enough to earn over £50kpa whilst also being modest enough in their lifestyle expectations to be able to live on £30kpa and so have money left over to be able to make such choices.
I also wonder why socialists who choose to buy private dental treatment or private medical care never get to bear the brunt of this kind of criticism?