Or is it the power that is limited? (Which makes a lot of sense)
There is almost always a power limit, and there are often spread spectrum, usage type, antenna directionality, and other requirements. Additionally, licensed users need For 433 MHz in the US, you have two allowed usage rules: 47 C.F.R. 15.240 [0] and 47 C.F.R. 15.231 [1]. The former is for transportation use only. The latter is what car remotes use, and your usage probably falls under that as well. Among other requirements, you can transmit for no more than 5 seconds--unless they are signalling an emergency alarm condition. If you don't follow either part there is a very minimal power output that is generally not useful for wireless data transmission.
[0] https://www.law.cornell.edu/cfr/text/47/15.240 [1] https://www.law.cornell.edu/cfr/text/47/15.231
If it's an FCC class B, YOU must accept interference from otherwise approved class B compliant devices. Class B is a very low threshold for that. Mostly it's power limits and not much else.
Key fobs, if you look at the fine print, are Class B.
There are also exemptions for certain experimental or lab devices though you can't break power limits with those as narrowly defined by regulation.
But if you happen to have your Class B device too close such a device, that's entirely your problem, the user of the Class B device.
This is a common issue with ham radio: they actually are allowed to interfere with Class B but it's a political decision that drives most of ham radio to "play nice". Legally they have seniority when it comes to interference and the law when it comes to Class B devices. Basically you are screwed with Class B in most cases with little legal recourse.
And Class B is such a low threshold that 99% of the time such interference is actually due to bad design or use of cheap components in the Class B device itself. In this case, the fobs. Same goes for TVs, broadcast radio receivers, etc.
No one has a right to zero interference from other RF sources for the most part! Mostly because it's physically impossible to assure or deliver! There's merely a regulatory threshold for the extremely bad and summarily interfering levels of RF power.
Regardless of class, spurious emissions are not permitted.
If i remember correctly the main two are: - Power limits - Transmission length per interval of time (I believe max 300ms in any 10s window)