Is kissing allowed with coeliac disease?

Yes. Current research suggests that kissing poses a very low risk of gluten exposure for people with coeliac disease. 
In a recent study of couples where one partner had coeliac disease and the other did not, researchers found that the transfer of gluten through kissing was minimal in most cases, even after the non-coeliac partner had eaten a gluten-containing food. 
To further reduce the risk, the study found that having the gluten-consuming partner drink a small glass of water before kissing lowered the amount of gluten transferred to levels considered gluten-free in all tested cases.
While there is no need for extreme precautions, it may be reassuring to wait a few minutes after eating or have a drink of water before kissing if one partner has recently consumed gluten.
So, the good news is: you can enjoy kissing without worry - gluten transfer through kissing appears to be very low and unlikely to represent a significant risk for most people with coeliac disease.