This is going to be a situation where there will be no fixed rule. One important factor is how meaningful colour differences are to the other parts of your problem. If colour has low correlation/impact in a supervised learning/prediction scenario for example, and the dataset is noisy, then you will want to merge more colours (at a higher fraction of total number) to reduce sampling bias effects that might otherwise assign importance to the colour and increase error rates in test and production.
The safest approach is to treat the colour combination threshold as a hyper-parameter to the model building process, and test to see what differences it makes. If there is little or no impact to model effectiveness, then a higher threshold could be useful purely to reduce number of parameters in the model - decreasing resources used to train and run it.
If that seems time-consuming, then picking something by feel (e.g. your idea of picking count less than 50 in the dataset) is not usually too bad, at least to start with. You can go back and re-evaluate your choice if you have problems with the model.
One other possibility for feature engineering is to use the rareness of the specific colour as an additional feature. So in addition to categories for the popular colours and an "other colour" category, add a real value "colour frequency" = the observed ratio of that colour in the training set. Whether or not this is useful will depend on the problem, but it may help address some of the lost information when merging categories with a wider range of rareness values, assuming that unusual colours indicate anything at all (they may not).