[minimal]

I don't understand this is in the slightest.  A Histology book that I'm reading, and this website (http://medical-dictionary.thefreedictionary.com/dye) seem to suggest that cationic is synonymous with basic, and anionic is synonymous with acidic.  This makes absolutely no sense.  While a carbocation might be a hydrogen acceptor, it is missing one/two electrons, so it is not a proton acceptor. 
Can someone clarify this for me?

[azmanam]

Can't clarify but I'll try to suggest some insight (although I have no proof to back this up):

Since the post you linked to gives the definition of dyes - and that definition includes

capable of coloring substances to which it is applied

perhaps the authors are trying to suggest that anionic dyes are will color acidic materials.  That is, if you have a basic material, an anionic dye will not color that material.  But an acidic dye might.

It's a stretch, and the dictionary is certainly not clear on this issue.

[minimal]

I had thought that at first but it seems both the dictionary definition and the book mean otherwise.  Here are some quotes from the book, "When staining with a basic (i.e. cationic) dye this will occur on substrates of high negative charge density..." or "Anionic ('acid') dyes, such as Eosin Y or Orange G, are rather less soluble in alcohols."
The thing about Eosin is that it is itself an acid, to quote wikipedia "Eosin also stains red blood cells intensely red. Eosin is an acidic dye and shows up in the basic parts of the cell, ie the cytoplasm."  So it cannot mean the substrate upon which it is acting, they are clearly referring to the dye itself.

[azmanam]

Thanks for providing the quotes.

Still can't offer a definitive answer, but here's what I see.

substrates of high negative charge density

While not the textbook definition of a base, high negative charge densities are indicative of good nucleophiles - and potentially protic bases.  The book has essentially defined the substrate to be non-acidic (although not necessarily basic). 

The thing about Eosin is that it is itself an acid

Actually, it is a base.  Check out that wikipedia page again.  The phenolic O^- in the lower left and the carboxylate COO^- makes this a dibasic compound (probably as the disodium salt, although that is not made clear.  Same with orange G.  The two sulfate SO₃^- groups make this also a dibasic compound.  (It is also technically amphoteric, as the phenolic OH group can act as an acid with a pH ~10)  Wikipedia does mention orange g is typically a disodium salt.

Based on your quotes, I'm going to stick to my answer.  While I have not found anything unambiguous online, Eosin Y and Orange G are most definitely bases, and substrates of high negative charge density are unlikely to be strong acids, and more likely to be bases themselves (and thus will react with your cationic dye - an acid by itself).

[minimal]

Thanks for providing the quotes.

Still can't offer a definitive answer, but here's what I see.

substrates of high negative charge density

While not the textbook definition of a base, high negative charge densities are indicative of good nucleophiles - and potentially protic bases.  The book has essentially defined the substrate to be non-acidic (although not necessarily basic). 

This cannot be the case though.  The book equates basic with cationic quite clearly.  Thus to say (and I agree) that the substrate with the negative charge density is likely a base, and that is definitely not a cation.  And why would a base stain a base?

The thing about Eosin is that it is itself an acid

Actually, it is a base.  Check out that wikipedia page again.  The phenolic O^- in the lower left and the carboxylate COO^- makes this a dibasic compound (probably as the disodium salt, although that is not made clear.  Same with orange G.  The two sulfate SO₃^- groups make this also a dibasic compound.  (It is also technically amphoteric, as the phenolic OH group can act as an acid with a pH ~10)  Wikipedia does mention orange g is typically a disodium salt.

Based on your quotes, I'm going to stick to my answer.  While I have not found anything unambiguous online, Eosin Y and Orange G are most definitely bases, and substrates of high negative charge density are unlikely to be strong acids, and more likely to be bases themselves (and thus will react with your cationic dye - an acid by itself).

I think I may have actually found the answer.  But I'll still need some help in deciphering it to make sure it's proper.  I was looking through another histology book, and I found this..."electrostatic bonding is influenced by the pH of the solution.  The pH of most alum hematoxylin solutions ranges from 2.2 to 2.9.  This pH lies above the isoelectric point (IEP) of nucleic acids, since the IEP of nucleic acids occurs in the pH range of 1.5 to 2.0.  The nucleic acid will therefore dissociate to give a greater number of negative charges to increase staining with the positively charged dye lake."

From how I understand it, is that it is both basic and it is cationic, but only within the extremely acidic pH range that they're working within?
Thus the same would be said for eosin.

[Yggdrasil]

At physiological pH (pH 7), basic compounds (e.g. amines) tend to be protonated, making them cationic, and acidic compounds (e.g. carboxylic acids) tend to be deprotonated, making them anionic.  This is confusing because these cationic species (e.g. ammonium ions) represent the conjugate acids of the bases, and the anionic species (e.g. carboxylate ions) represent the conjugate bases of the acids.

[minimal]

Excellent thanks for the response.  My question is why do they then not simply say the conjugate acid or base for whatever respective base or acid? Because surely The ammonium ion is not really going to act as a base (barring extreme circumstances), correct?

[Yggdrasil]

Because they're biologists and they don't know/care about the details of the chemistry.