Sort of. It's more like one side is being inconsistent because the other side has given them adversarial license to do so by also being inconsistent, but in the opposite direction. Both sides should want common-carrier regulation for both residential ISPs (Comcast) and OSPs (Twitter).
There's also a related problem in which both sides not wanting something their constituents want will use each other as an excuse to not do the thing. For example, Right to Repair polls very favorably with basically anyone, but politicians do not want to touch it with a 10 foot pole. It is an "antipartisan issue", one that has popular support but bipartisan opposition. One way you can kill an antipartisan issue is by turning it into a partisan one, so that your side's supporters shut up about it and the opposing side's supporters are deadlocked by yours. There have been attempts to do this by R2R opponents, by say, telling angry farmers that R2R actually only benefits rich, MacBook-toting liberals.
There's also a related problem in which both sides not wanting something their constituents want will use each other as an excuse to not do the thing. For example, Right to Repair polls very favorably with basically anyone, but politicians do not want to touch it with a 10 foot pole. It is an "antipartisan issue", one that has popular support but bipartisan opposition. One way you can kill an antipartisan issue is by turning it into a partisan one, so that your side's supporters shut up about it and the opposing side's supporters are deadlocked by yours. There have been attempts to do this by R2R opponents, by say, telling angry farmers that R2R actually only benefits rich, MacBook-toting liberals.