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Probably a strange question, but I don't want to have an ugly house. I
have put down baseboards in the 3 bedrooms of my house, and am getting
ready to do the LR and DR (it is a rambler with the BRs on the same
level as the LR and DR). For the BRs I used plain one-piece baseboards
from the BORG.

For the LR and DR, I am wondering if it would be tacky, detract, or
somehow look out of place, if I used fancier baseboards, such as 2
piece - base and base cap? I seem to have the idea that a theme should
be common throughout a house, but then I have a lot of misconceptions in
life. The 2 different types of baseboards would never meet, since the
BR doors separate them.

What you propose is done all the time. Go for it. Many spend more
money (nicer materials, nicer details) on the LR and DR than the
the kid's bedroom.