I think it would be considered offensive, but not for the reason that you seem to imply (a double standard and that racism among blacks is OK).
White people are the majority. As the bulk of the American television audience, they are the implied audience for TV unless stated otherwise because there are simply more of them. Black folks and people who primarily speak Spanish are in the minority. If most TV is being aimed at the primary audience (white people), then, assuming that there are differences in preferences for the type of material shown between these groups (which there are), it’s profitable to target this niche with programming directly aimed at them. However, you need to get the attention of said group in order to do so. That’s where BET gets its name. Now I’m sure the folks who run BET would be perfectly happy if lots of white people and Spanish speakers and whoever else started watching, because it makes them more money and they don’t mean to be exclusive.
Now, to call a station “White Entertainment Television” makes a different implication because white people are the majority and, therefore, the default audience. It reeks exclusivism and therefore would be taken as offensive.
The same would apply for other minority/majority divides. For example, having magazines targeted at gay people (like The Advocate) is acceptable as not offensive; however, turning around and having a magazine target the majority audience (straight people) would be offensive, because, generally, magazines imply having a mostly straight audience. Hence, I see no reason for straight people to understand that mainstream media focuses on them, and therefore there is a market for gay segment of the population. If gay magazines are slamming straight people, then there is grounds for offense.
This is not a double standard. There is simply an obvious difference in how we treat terms racially. “Black pride” and “white pride” give off vastly different vibes to Americans who hear those terms. This does not mean that minorities are given license to be racist; it means that racism is implied in one term and not the other. Were that to change, WET might become societally acceptable as not being associated with racist groups.
For now, however, we must accept that racial differences in terms and treatment do exist. To say so does not make me a moral relativist – I simply can’t ignore that there are these differences in tone and meaning.
I suspect that in the future these terms will be less and less necessary. In the meantime I do not think BET needs to change it’s name. A reasonable person understands that there is no racism implied in the name and so there is no offensiveness. You can argue that it SHOULD be offensive, but it isn’t; therefore, there can be no “double standard”, no “special allowances”, and