There are many digital mastering effects and/or plug-ins available to the serious hobbyist and mastering engineer which are designed to make a digital track sound "analog", especially to have such tracks have the sound of saturated analog magnetic tape. I've used some of these plug-ins myself in Wavelab from Steinberg, and when used judiciously, they do impart the soft highs and warm mid-bass often associated with older analog tape recordings.
Back when I had a vinyl setup, I recall buying several of the Telarc LPs which were obviously recorded digitally, and commenting how wonderful they sounded. Some other digitally recorded LPs of the time were shreeky and just plain nasty.
Like so many of these debates in Audiophile-land, it's the actual execution that matters most, not the medium, media or whether the recording is analog or digital.