I got this info on the tofutti website, includes some detailed info about
how they produce their products.  I found it interesting, especially since
they do produce on shared lines and yet have a k-parve listing for all
their products:

I know all Tofutti products are Kosher Parve, which means that they
contain no dairy. However, I was told that some of your products are run
on equipment that also runs dairy products. If this is so, how are your
products dairy free?
Although we would wish it otherwise, the overall demand for totally dairy
free products is not large enough to justify setting up complete
production lines for dairy free products only. Most plants we use for
manufacturing our products mainly produce dairy items. This is true for
all companies who sell dairy free products, no matter who they are. In
addition to the normal plant sterilization, cleaning, and testing
procedures, we employ a kosher supervisory service, the Kof-K, to
supervise the manufacturing of our products to ensure that they are
completely dairy-free every time. The methodology and techniques they use
to clean the equipment and supervise the production is the process called
kosherization. Kosher Parve means that there are no milk (or meat)
derivatives in our products. It also means that the equipment used to
produce Tofutti is either dedicated to non-dairy products or has gone
through the rigorous sanitation and cleaning requirements of kosherizaton.
In the typical plant, the equipment is washed and sanitized with a caustic
rinse and an acid rinse. The caustic rinse is done with water at boiling
temperature (212 degrees Fahrenheit). This is followed by a boil-out with
pure water. There are several other components to the sanitation, but they
are not listed as they do not affect the kosher status. A rabbinical
supervisor is present to independently verify that these procedures are
being adhered to and to review logbooks and digital records to verify that
these procedures are followed.

If you feel that the preceding information raises your concerns about the
safety of our products regarding dairy contamination, please do not use
our products. Safety of our consumers is always our number one priority.
For further information about kosher, please refer to our previous
discussion on the subject.