Is there a word for "automatic" with negative connotations?

This is what the question says (emphasis mine):

a policy of automatically renewing subscriptions without any warning or notification that the subscription is up for renewal.

This means that you have already agreed that there will be an automatic renewal. There isn't anything shady going on that a renewal happens without you having known that would be the case.

Therefore, the emphasis is on the renewal itself, rather than the motivations of the company behind it.

Some companies do provide advance notice that something is about to be renewed. It gives you a chance to cancel your subscript if you wish. Without that advance notice, you can have forgotten about it and miss the chance to cancel (assuming you want to).

How could the quality of the this automatic renewal be expressed? It is abrupt:

[Merriam-Webster]
1 a : characterized by or involving action or change without preparation or warning : sudden and unexpected
      // came to an abrupt stop
      // an abrupt turn
      // an abrupt decision to retire
1 b : rudely or unceremoniously curt
      // She has an abrupt manner.
      // an abrupt reply
1 c : lacking smoothness or continuity
      // an abrupt transition

A possible sentence used to describe the situation in the question is the following:

Without a friendly reminder ahead of time, we find your automatic renewals to be abrupt.

Anything that is abrupt has a negative connotation. As in the definition itself, it is sudden, unexpected, rude, curt, and lacking advance notice.

OED:

pre-emptive, adj. and n.

3. Military. Of an offensive strategy or action: intended to forestall an enemy attack; frequently in pre-emptive strike (now frequently figurative).

In its figurative sense it carries the nuance of an action taken suddenly in anticipation of, and to counter, the third party's possible action:

OECD Economic Surveys: Mexico 2007 - Page 11 "The bank responded with a pre-emptive move by raising its interest rate in April, in order to prevent the upturn in inflation from feeding into inflation expectations."

In your context, "pre-emptive" would be have the nuance of "reprehensible."

1. peremptorily

in a way that expects to be obeyed immediately and without any questions. https://dictionary.cambridge.org/dictionary/english/peremptorily

2. robotically

Then he was mocked for robotically repeating the same answer during a television interview. Times, Sunday Times (2011) https://www.collinsdictionary.com/dictionary/english/robotically

blindly (adj.)

• 2. Without understanding or using one's judgement; unthinkingly. ‘don't blindly accept dogma as justification’

From that definiton, "unthinkingly" would also fit your purposes. If your complaint is primarily that there was no notice, "silently" fits the bill, but doesn't convey the "without thought" part. British English speakers sometimes use "blithely" to describe unthinking actions, but it's rare in American English.

To convey your frustration that the action was not one you were given a chance to agree to, consider

Unilaterally (adj.)

• undertaken or done by or on behalf of one side, party, or faction only; not mutual

However, using a single word will reduce the emphasis on that aspect of your complaint. If there's a particular aspect of behaviour that you are unhappy with, it's usually better to state it in full. In your example, try this:

• automatically renewed this subscription without first obtaining our consent.

This also explains the behaviour you were expecting. (You can of course replace "automatically" with any of the suggested adjectives)

Performing an action like a drone. Drone like, mindless and without any thoughts.

Edit Adding supporting reference as suggested by TCooper

Definition 2 of dronelike from Wiktionary, which is a synonym of mechanical

Definition 3.1 of drone from Lexico.com

In the latter, a usage example is ‘Oh, you're right, they do sound like mindless drones when they greet you, Toni!’

Mechanically

Without thought or spontaneity; automatically. ‘the words are repeated mechanically’

How about covert autopayments? From Lexico:

covert: Not openly acknowledged or displayed.

When a company charges you automatically, especially for a long period of time, for services you no longer use, and it does so without letting you know this is the case, e.g., by sending you regular itemized bills or querying you re your extended non-use of the service, they are not openly acknowledging or displaying that they're continuing to charge you. I'd call these covert autopayments.

Surreptitious autopayments would also work (see Conrado's comment on your question). From Lexico:

surreptitious: Kept secret, especially because it would not be approved of.

While one could argue that such autopayments are not entirely secret, the automatic charging policies of some companies certainly demonstrate a major, if not intentional, lack of transparency.

While I am a firm believer in "Caveat emptor," I considered my Netflix experience (see my comment on your question) to be an unscrupulous business practice (see Jim's comment on your question). From Lexico:

unscrupulous: Having or showing no moral principles; not honest or fair.

Compulsive is a reasonable fit here.

It means that something is done due to an irresistible urge or force rather than a conscious desire.

"Your policy regarding compulsive renewal is unjust..."

I'm not sure if this entirely fits the negative connotations part, but consider

preordained

From the Cambridge Dictionary

to decide or fix what will happen in a way that cannot be changed or controlled

I feel like this suggests more consciousness to the inevitable action than automatic does, which may arguably be more amenable to negative connotations.

I think rote does well here.

From Merriam-Webster

rote 1: the use of memory usually with little intelligence learn by rote 2: mechanical or unthinking routine or repetition a joyless sense of order, rote, and commercial hustle — L. L. King

I like

• tacit

And I prefer

• senseless / mindless

over "blindly" because I don't see a need to conflate sightedness with thoughtfulness.

Knee-jerk is defined by lexico.com as

(of a response) automatic and unthinking.

I think Programmed does bear a negative connotation when applied to humans. Similar use can be found here

Another term Hardwired may also convey similar yet not exactly same meanings

Doing something "on auto-pilot" can have a negative connotation. Doesn't exactly apply to the auto-renewal example, but "going through your day on auto-pilot" is a bad thing.

Unbidden

not invited or wanted

Even though it isn't exactly the same as automatically, it could be used as a negative connotation of the same to signify that the action was performed without consideration and/or explicit request and was perceived negatively because of it's undesirability.

repetitive

This word is usually used with negative meaning.

"Repetitive work tires the worker."

"Repetitive strain injury"

It does not convey the meaning of "automatic" in the sense that something happens without human intervention, but the context could convey that.

"The repetitive confirmation dialogues from the software annoy me."

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Note: I am aware that "repetitive" is not a synonym for "automatic". It might fit the bill in a context where the automatic nature is implicit.

In the same spirit as one of the answers above, there is also mechanistically, which I think is slightly more pejorative than mechanically.