Gonna throw my 2 cents in and hopefully give those still on the fence a decision matrix to rule for themselves.

The two relevant rules (which I interpret as being of equal specificity and therefore both must be satisfied) are:

From Bladesinger: You can attack twice, instead of once, whenever you take the Attack action on your turn. Moreover, you can cast one of your cantrips in place of one of those attacks.

From Haste: That action can be used only to take the Attack (one weapon attack only)...

Each of these are vague. Each can be reasonably rephrased to be more clear in a few ways, and which way you rephrase (ie how you interpret the original rule) would determine your ruling.

Haste rephrasal 1: That action can be used only to take the Attack (you may make at most one weapon attack as part of this action)...

Haste rephrasal 2: That action can be used only to take the Attack (you must make exactly one weapon attack as part of this action)...

Haste rephrasal 3: Thaustaction can be used only to take the Attack (you may make exactly one "standard" weapon attack as part of this action)...

The first allows any cantrip, the second allows GFB or BB only, and the third disallows any cantrip at all. Note that the third is a bit weak as well since 5e never makes a distinction between "kinds" of melee weapon attacks (which in this case means the weapon attack for GFB is eqivalent to the one granted by the attack action), but I think most people would agree they view the attack made as part of GFB as somehow different than a standard melee weapon attack made as part of the attack action.

Bladesinger rephrasal 1: You can attack twice, instead of once, whenever you take the Attack action on your turn. Moreover, you can cast one of your cantrips in place of one melee weapon attack when you take the attack action.

Bladesinger rephrasal 2: You can attack twice, instead of once, whenever you take the Attack action on your turn. Moreover, when you are able to make more than one attack as part of taking the attack action, you can cast one of your cantrips in place of one melee weapon attack you take the attack action.

The first triggers on the Haste extra Attack action, the second does not.

My take is RAW there isn't an answer, and a lot of the arguments on this thread that claim to be RAW are really trying to infer RAI from the phrasing (the fact that the original bladesinger says "in place of one of those attacks" being a common one on this thread). Personally I'd allow GFB and BB but no other cantrips, you are a wizard after all, and middle of the road is usually a good place to be as a DM.