I have the same issue if I run all Musgo, all the time. No problems with the a/s splash but I can't run the Classic cream very often. I must have an issue with lanolin
Some people do have a sensitivity issue with lanolin, and you could be one of them. But on balance, far more people have issues with scent. All the EU regulations on scent, which result in reformulation of popular colognes and such, are due to the fact that scent sensitivities are fairly common. Just based on the numbers, I'd say it's more likely you and Mormon Bridge are reacting to the fragrance in the Musgo cream, rather than the lanolin. FWIW, I also have a comfort issue with Musgo Classic (it tends to sting a bit on the second pass), and yet I have not had any issues with any other products containing lanolin. I presume it's the strong scent that my skin doesn't like. (Too bad, since my nose loves it.)
Side note: The Paula's Choice website gives lanolin a "good" rating, and notes a study published in the British Journal of Dermatology that says the overall percentage of test subjects who demonstrated a lanolin sensitivity was quite low (1.7%), and was lower still for products that have a lanolin concentration of 50%. Conversely, the folks at Paula's Choice are always advocating against using skin care products that contain scent, due to their likelihood to cause sensitivity issues.