Does Segwit mean easier government monitoring? I have noticed a steady stream of PR articles talking ad nauseum of the dangers of a contentious hard fork and how miners refusing to signal segwit are screwing us all. Many are quite well written and read like propaganda to me, so I am naturally suspicious of their intentions and motives.

I see many talking about investors that have a long position in BTC, also founders of startups that seek to open up a market for sidechain solutions. My understanding of segwit is that by moving witness data aside, then third parties no longer have the ability to change a tx id, which gave me the realization just hoe hard it would be to monitor the blockchain for specific transactions.

Would it be safe to assume that law enforcement or governmental entities are having a difficult time tracking criminal behavior because of this and that segwit would make their investigations significantly easier and less complicated? By adopting segwit are we abandoning what little anonymity remains in Bitcoin or am I missing something important?
No, that's completely wrong. There is absolutely no anonymity benefit to third-party transaction malleability.

Third-party transaction malleability makes use of a symmetry in ECDSA signatures that allows changing a transaction's id to exactly one alternative id. The alternative signature has been deprecated and non-standard for years, but miners could still confirm a malleated transaction if they chose so. In fact, it's rather simple to convert transactions from one txid to the alternative txid, and this happened recently, when Bitclub mined a few malleated transactions. Besides a few poorly coded websites suffering hiccups, this was largely a non-issue. However, this issue currently delays use-cases that rely on chains of unconfirmed transactions which would be broken by a malleated transaction in the middle of the chain being confirmed. 

Transaction malleability is completely irrelevant for tracking, because tracking typically happens after the transaction is confirmed and therefore has already become immutable. Since the connection is made via following from transaction outputs to outputs, there is no hindrance whatsoever due to a malleated transaction.