Storing sourdough starters with wine in a wine fridge?
My starter is going on 6+ years old now.  I keep it in the fridge in a covered container.  Of course, it would be slightly warmer in a wine fridge, but I would also recommend a covered container in that situation too.  There will be a little activity, but not enough for gas to escape.  In this scenario, I remove a portion of the starter, add new flour and water, and return to the fridge approximately weekly.  I have gone much longer between feedings with no harm...as long as I give it plenty of time to build up before use (at least a day on the counter...sometimes two if I've forgotten about it in the back of the fridge).  In any case, it will not impact your wine.