Distinctions between experts
We need to draw some distinctions. A surgeon is an expert whose special and specialised knowledge is verifiable and has been confirmed in definite ways - we have firm criteria of success. This is a generalisation but largely true.
The widespread popular complaints against experts centre on professions or practitioners who cannot reliably accomplish what is expected of them. Political scientists largely and indeed overwhelmingly failed to predict events in the Soviet Union in the late 1980s and early 90s. Economists (largely) failed to predict the financial crisis of 2008 and unlike a surgeon dealing with a heart attack patient had rival remedies not based on any body of consensual knowledge of the kind on which heart surgery relies.
Criticism of experts can also rest on unrealistic and unfair assumptions of what level of accuracy different expertises can offer in their current state of development. 'Experts ! You can't even trust weather forecasts'. In fact you largely can trust weather forecasts at the level of detail on which they operate. A meteorologist can't say whether it will rain in my part of town next Wednesday at 10 a.m., but almost certainly can successfully predict the range of temperatures over the UK in the next two days.
Summing up so far : there is no inconsistency, let alone hypocrisy, in trusting experts in one field and distrusting them, or adjusting what we can reasonably expect from them, in others.
The place of experts in a democracy
But there is another dimension to your question. It concerns the problem of trusting experts beyond their expertise. There used be calls in the 1930s- 50s for 'a government of businessmen (sic)'. And we still catch the phrase, 'UK PLC'. The UK, the USA, the EU and other political units are not economic enterprises and they cannot be properly run as such. Politics is not a matter of profit maximisation, higher productivity, the minimisation of costs.
Even if the business community has commercial expertise, that expertise is of limited relevance to politics, certainly to democratic politics. Economic resources set limits to politics - to what is politically practicable - but we cannot make normative political decisions purely by reference to them. If I want to know at what age (if any) to set retirement, I need data on economic consequences but not only such data : non-economic values enter crucially into this decision - as they do as regards the kinds and levels of medical provision for the elderly or the terminally ill. 'The expert [here the the entrepreneur or the academic economist] should be in tap but not on top', as Harold Laski said. Our political plans and arrangements have to operate within our economic means, at least over the long term, but how to run politics within those means is not a matter for commercial experts or experts in academic economics. It is the proper domain of collective decision-making.