Is it necessary to separate DC power cables and data cables?

The answer is "It all depends".

• What is the load on the DC? If it's very noisy inductive loads, you're going to have noise on the DC line, and it might be considerably more than you'd think
• What is the signalling rate on the data lines? Faster rates are vastly much more sensitive
• [EDIT] What line encoding have you got? Anything differential, such as RS-485, is going to be a lot more robust than something voltage-based, such as RS-232

• What coding scheme are you using? If you have got any scheme with error detection, perhaps it will be ok

• What happens if there are errors on the line? If it is updating a clock display, with the effect of a little time skew that's different to dropping heavy machinery onto workers.

Having said all that, it is quite common to have signal and DC power adjacent. I have quite a lot of underwater telemetry where we use specially-made DC-power and twisted pair cable for 24 VDC and 250 Kbit/s RS-485. In another much more noisy environment we use 9600 bit/sec. Per commenters, of course power-over-ethernet is one of the best examples of high-speed, long-distance, high-power DC and data in the same cable. (Long and high compared to for example USB or a bus on a PCB. 100 metres, 12 Watts.)

In short: it's perfectly doable, but pay good attention.

The current drawn over a DC power supply is usually not constant. Changing current results in a changing magnetic field.

So it might be necessary to separate power and data, it might not be. In USB or PoE Power and data are not separate. In SATA it is.

So you might need to take measurements and either separate the cables or get a better shielding between power and data.

Honestly AC vs DC isn't really very relavent.

There are two reasons to seperate power from data lines.

The first is safety. Voltages above 50V or so can be a shock risk. Currents over a handful of amps can be a fire risk. For this reason electrical regulations often require either a certain seperation between mains and communication circuits or extra precuations to be taken (such as earthed metal barriers or mains rated insulation on both the power and communication lines, exactly what is and isn't allowable will depend on what standards you are working to).

The second is interference. As you say constant DC isn't going to couple into your communications lines. If you have gone for a half-decent twisted pair for the data lines then 50Hz is unlikely to be much of a problem either. The real problem is the transients and interference that all too often end up superimposed on power wiring. How bad this is will depend very much on the characteristics of your supply and loads.