The cavalier's Order may be a problem
Druids are required to revere nature (as noted in the Ex-Druids section in the Core Rulebook), have Neutral on at least one axis of their alignment and not teach Druidic to non-druids. For some Orders this is fine, for example the Order of the Beast has such a similar philosophy that it is easy for a druid / cavalier to be true to both class requirements.
The potential for internal conflict arises where the precepts of an Order do not match with the druid requirements. For example, if the druid / cavalier is in the Order of the Lion they must be completely loyal to their sovereign. If the sovereign respects nature, all is well, but if the sovereign starts rounding up wild beasts, slaughtering them and using the remains to raise an army of undead, then the druid / cavalier cannot be true to the requirements of both classes. Similar conflicts have the potential to arise with some of the other Orders and/or situations.
However, given a philosophically compatible Order there is nothing in the material I have read that suggests that the cavalier and druid classes are inherently incompatible. (A brief glance suggests that multiclass druid / cavalier may be underpowered at medium to high levels, but that is outside the scope of the question.)