As of the 2013 edition of ASME B16.5, the scope section explains:
This Standard states values in both SI (Metric) and
U.S. Customary units. As an exception, diameter of bolts
and flange bolt holes are expressed in inch units only.
These systems of units are to be regarded separately as
standard. Within the text, the U.S. Customary units are
shown in parentheses or in separate tables that appear
in Mandatory Appendix II. The values stated in each
system are not exact equivalents; therefore, it is required
that each system of units be used independently of the
other. Except for diameter of bolts and flange bolt holes,
combining values from the two systems constitutes nonconformance
with the Standard.
This is actually a pretty common practice where metric and inch systems are regarded separately. While the numbers may not match exactly, the intention is that they work as a system within each unit of measure. Of course, as far as I'm aware, you would not buy a metric flange for an NPS or DN size pipe separately, they will be the same product manufactured to some company's internal drawings, so in essence the standard is accepting that any rounding errors are within tolerances intended by the standard. One reason they don't allow intermixing when interpreting the standard is that they don't want you to be able to cherry-pick the most permissive set of dimensions and tolerances for each feature.
The forward also notes:
The 2003 Edition included metric units as the primary reference units while maintaining U.S.
Customary units in either parenthetical or separate forms.
So it would be reasonable to consider the metric information in the standard to be slightly more authoritative than the inch information.
The forward to ASME B36.10M-2004, which covers the dimensions of the actual pipe, explains
The standard was revised in 1978 to include SI metric dimensions. The outside diameter and
wall thicknesses were converted to millimeters by multiplying the inch dimensions by 25.4.
Outside diameters larger than 16 in. were rounded to the nearest millimeter, and outside diameters
16 in. and smaller were rounded to the nearest 0.1 mm. Wall thicknesses were rounded to the
nearest 0.01 mm. These converted and rounded SI metric dimensions were added to Table 2. A
formula to calculate the SI metric plain end mass, in kilograms per meter, using SI metric diameters
and thicknesses was added to section 5. The SI metric plain end mass was calculated and was
added to Table 2. These changes in the standard were approved and it was designated an American
National Standard on July 18, 1979.
So they do acknowledge some use of rounding. For 2" NPS pipe they list the OD as 2.375 inches and 60.3mm (DN 50 size.) There there is only an error of .025mm which is consistent with their rounding philosophy. While your observed error of .152mm is definitely larger than I can directly justify, it is unlikely to cause a serviceability issue in a welded joint - .006" in below the manufacturing tolerances of most metal parts that are to be welded. Tolerances that small are usually achieved by precision machining. I would not be concerned about the actual function of the joint.
To address your specific question in the title, the pipe should be sized according to its own spec. That standard may have its own dimension tables, or it may reference ASME B36.10M and then specify manufacturing tolerances on top of it. In the US, if you'r ejust looking at plain black pipe, the relevant standard would be ASTM A36, but a multitude of standards exist for other materials, tighter tolerances, and application-specific pipes.