First things first, this is not remotely common from anything I've seen and I've reviewed a lot of employment agreements in M&A contexts.
Second, I'd be curious what they are referring to as "disparagement." Is that defined in the agreement?
Third, I'm not sure what state you are in, but that might matter. I haven't researched the issue and there may be case law already. But my guy instinct is that this would violate public policy in a state like California, perhaps depending on what "disparagement" is meant to mean.
I'll give you one reason why. California, as you might know, is very hostile to restraints on ability to pursue a profession (most notable example - non-compete agreements). If you cannot disparage your employer post-employment, that may make it impossible to compete with them.
Of course, this depends on what disparagement means. Absent contract, the main restrictions on commercial speech that "disparage" a competitor are in the world of defamation and trade libel law (on a state level) and the Lanham Act/unfair competition law (largely on a federal level). This is gross oversimplification, but good enough for the moment.
Those laws generally require proof of falsity or misleading nature of the underlying speech.
A non-disparagement clause, on the other hand, is a contractual obligation that goes further than that. It CAN, depending on the wording, extend to truthful speech. And it often does.
Competitors need to be able to distinguish their products and services from each other - most notably in ways that promote their own services as "better" than the other or by noting flaws in their competitors products and services. This is part of healthy competition. Defamation, trade libel, and unfair competition laws all permit this.
But it's not necessarily possible with a non-disparagement clause. And, therefore, the ability to compete fairly is materially diminished.
I would note that even in California, there are exceptions to the public policy ban on non-competes in the M&A context. And that might be read to extend the public policy concerns around a non-disparagement clause. But the contractual terms need to be narrowly tailored. It has to terminate at some point. Perpetual restrictions are not enforceable.
TL;DR: This isn't normal. You're not overreacting.