"As Philip Dawid once said "a causal model is just an ambitious associational model". A carefully-considered regression model, with an appropriate set of potential confounders (possibly identified using a causal diagram – see below) measured and included as covariates, is the most appropriate causal model in many simple settings."
To paraphrase Angrist and Pischke:
To the extent that the population CEF that it is estimating is causal, so is linear regression. (And that includes LPMs)