Why was this transaction accepted even though it was a double spent attempt? Txid: eb37a52fbd74a77f14836a926c58cdc1543759553fdd2e058c6da9e1e1aa5089
I'm not sure, but maybe because another one was rejected. It says "Double spent attempt detected. From tx: 0d6e868d89c5b64a22aeafda249bb75cb53656cba092531f126f350b73a7e307,1" And this second transaction does not exists: https://mainnet.decred.org/tx/0d6e868d89c5b64a22aeafda249bb75cb53656cba092531f126f350b73a7e307
So this is more of an issue with mainnet.decred.org It falsely flags certain transactions as double spends from time to time. We have plans on revamping the entire service (insight) in the future. In the end we always recommend using dcrd + dcrctl getrawtransaction <txid> to get correct information about a transaction.
More specifically, it seems to retain the information in orphan blocks and then flags them as double spends since it sees transactions in both the orphan block and the block in the main chain.