Sloppy
I've already mentioned I'm not in favour of uniformed personnel taking part in gay pride, because it may lead to cynical photo ops, like the one we saw the other weekend. I'm not sure, however, there is a valid argument against such participation on political grounds.
All but the most banal deployment of uniformed military personnel is going to be "political" to someone. A republican (or for that matter, any taxpayer) might object to guardsmen being used to convey The Queen's personal luggage to one of Her Majesty's holiday homes. An atheist might object to military personnel attending a church parade at public expense. Almost anyone could take exception to a Tornado flying a display sortie at an arms show. The list is endless. Personally, I wouldn't see any harm in a uniformed presence at Notting Hill. BNP, Poll Tax and Countryside Alliance marches, however, have an overriding political purpose, rather than a celebratory one. I appreciate it is a fine line, but it's a case of like it or lump it, I'm afraid.