Which advocates in particular?
Why do you think buying a beach homes implies they don't believe what they are saying?
Are you arriving at the most convenient conclusion for yourself, rather than the most likely one?
Former president Obama stands out. Why would you spend a considerable amount of your wealth on a home that is about to be swallowed up by the ocean on account of us barreling headlong into imminent climate catastrophe? You wouldn't.
Climate catastrophe will not visit Martha's Vineyard within Barack Obama's lifetime. No one says it will.
Living on MV does not contribute to the climate problem, so his actions are not hypocritical.
If he was looking for a 100-year property investment, perhaps he should have chosen a different part of New England (elevation > X meters), the Pacific Northwest, or the Great Lakes region.
If he's looking for a nice, private, place to live for the next 30 years, MV has a lot going for it. He won't live there for 30 years of course, and maybe "leaving it to the kids" isn't high on his priority list, and maybe he even has a lingering hope that mitigation efforts will happen and succeed. He didn't get famous by being a pessimist (ObOnTopic).
And, sure is a good thing he didn't move to Florida or the desert West, where he'd be both more endangered and more contributive to the danger.
I really can't imagine any plausible explanation for how any person arrives at the "Obama says climate change is a problem, but buys house near beach, must be hypocrite and bad person" narrative, unless of course you started at the end and worked backwards.
(edit) ... which, I see from other comments, seems to be the case. You believe Obama is lying about climate change and that buying a house on MV is proof? OK. Amazing.
What is the definition of imminent? Maybe Obama thinks that he and his family will still get sufficient utility out of before the home is swallowed up by the ocean? Perhaps he feels he has enough set aside for his descendants and is comfortable blowing the rest on personal comforts for their remainder years?
Perhaps Obama is optimistic that we'll pull our heads out of the sand and do what we need to do to prevent his home from being swallowed up by the ocean.