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

Solution 1:

Mechanically

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

Solution 2:

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)

Solution 3:

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