My parents are of the same mindset, they are very supportive but completely against poker, my mother especially. It is not so bad that I cannot play in their presence but they would never support me going full time on it.
I find the main problems are stigma and ignorance.
Poker, amongst many people I would call the 'parents' generation obviously still assosciate it with being a shady past time etc so it is hard for them to take any pride in their child doing this.
Secondly, they know nothing of the daily ups and downs of poker, BRM etc etc, so they will always ask, "How much did you lose today?" not even how did you do, but "how much did you LOSE?" and if i say "well actually I made $XX today" they will fire back with "but how much did you lose to make that?" It is really frustrating, and they won't even bother trying to comprehend ROI etc etc
However, I combat this a few ways, I play pretty small stakes and it's all SNG's so I often pull up Sharkscope which (thankfully) shows a steady upward trend and they don't mind if I'm not risking too much. I also play it part time so they don't see it as me trying to make it my main source of income and until I do earn enough to live off it I will keep it that way.
I also have a GF who I am trying to convince and she is coming round to it and enjoying watching my sharkscope progress and is also starting to understand ROI and BRM concepts. I will be moving in with her soon enough and then I can play more seriously without the negativity around me.
Just be patient and if you play profitable poker then they will come around.