A recommendation frequently seen in past geological ages, but that I haven't heard recently was that sometimes "tape noise" is caused by excessive or irregular tension in the tape. It can also occur if a tape has been "on the shelf" for a while and the layers of tape in the reel are even slightly stuck to each other.

The recording medium is "bonded" to the carrier film, and as with any complex material, long term contact between "layers of stuff" can cause slight sticking. In the case of tapes, the pulling apart isn't likely to harm the tape but can cause some variation in the tension as the "sticky spots" are pulled into the feed.

When left "wound up" in the spool, the carrier film can also change its length, usually be shrinking slightly, so that the tape may be significantly more tightly wound if it's been sitting for a relatively long time.

A suggested possible, sometimes partial, cure was to just fast forward the tape to the end and then rewind before you start any critical listening or copying from them. For a tape that hasn't been played for a while, sometimes a couple of cycles of "retensioning" the tape this way will reduce the noise in the output signal.

The case material can also warp, or sometimes may have been a little crooked from the start, but since the part of the tape where the "listening" is done is in a fairly long free-running length of "just tape" the signal you get from it can be good even if the case itself squeaks and squawks with mechanical noises, a long as the tape itself moves at a regular speed past the heads. The cassette physical noise may be annoying when listening to a tape, but shouldn't be picked up in the signal that you record on a new medium - usually.

John