If eating milk and chicken is only a rabbinical prohibition, why don't we find that we are more lenient with regards to it. For example, why don't we wait less time between eating chicken and milk?
[the ice cream in my freezer looks good right now]
The reason why we see leniencies by rabbinic laws is because of the rule that we don't make decrees perchance that someone will come to transgress a rabbinic violation. (gezaira l'gezeira). But that is only when the 2nd decree is not related to the 1st decree. Sometimes when the rabbinic law parallels the Torah law, the chachamim will extend the decree to the rabbinic law simultaneously. This is what is referred to as "chada gezeirah hee".
An example of this can be found in Taz Y.D. 98:5. The Taz holds that if kosher and not kosher meat soups get mixed up, but then spilled and you don't know whether there was 60X kosher, but you know there was at least a majority of kosher, it is permissible because there is no case of min b'mino with a majority of kosher that is Biblically not kosher. So forbidding the safek would be a decree on a rabbinic prohibition.
However, kosher chicken soup and milk that got mixed and spilled and you don't know if there's 60X has a parallel case of meat and milk which is biblically forbidden under 60X. So the chachamim included this case when they forbade chicken as a gezeira, even though the worst case of this scenario is rabbinic.
By the way, we are lenient in some areas: you can cook chicken with milk and have benefit from it. Also, you don't have to wash between chicken and dairy.
Shulhan Arukh Y"D 87:3
אינו נוהג אלא (ה) בבשר בהמה טהורה בחלב בהמה טהורה, ג אבל בשר טהורה בחלב טמאה, או בשר (ו טמאה בחלב טהורה, <ב> מותרים בבישול ובהנאה. ד (ז) ה] ובשר חיה ועוף, אפילו בחלב טהורה, (ח) ו] מותר בבישול, ובהנאה; ואף באכילה אינו אסור, אלא ז] מדרבנן. ה <ג> אבל דגים וחגבים, אין בהם (ט) איסור, אפילו מדרבנן. הגה: ו ח] ונהגו לעשות (י) חלב משקדים ומניחים בה בשר עוף, הואיל ואינו רק מדרבנן). אבל בשר בהמה, יש להניח אצל החלב שקדים, משום מראית העין, <ד> כמו שנתבאר לעיל סימן ס"ו לענין דם.
4) Even basar chaya 3 [with milk] and chicken meat 4 [with milk] are mutar b’bishul and b’hana’ah. (3) 5) Furthermore eating chaya or chicken cooked with milk is only assur mid’rabbanan. However fish and locust that are cooked with milk are not even assur mid’rabbanan. There is a custom to allow chicken to be placed into almond milk because it [milk and chicken] is only assur mid’rabbanan but in the case of basar b'haima [with almond milk] one should place almonds next to the almond milk because of maris ayin 5 (4) as was explained in Siman 66 concerning blood.
The answer is that we are more lenient in some respects. The primary prohibition is on account of Marit Ayin. The other meforshim on the daf explain that the situation has to be two steps removed from the Biblical prohibition(such as the Rama says of chicken with almond milk) before we can drop all pretenses of the issur. So as regard to time waiting and such as that, when dealing with chicken and actual milk, we are still under the Rabbinic enactment to treat the eating of chicken with milk such as meat and milk in every respect.
We are more Machmir on D'Rabanan in order not to be Mzalzel
Ashkenazim consider the waiting to be a minhag, not a takana d'rabanan. It happened to be that the minhag developed to include both meat and chicken. According to the Rambam, its an actual takana, so one should check if he holds one has to also wait after eating chicken.