I think you can totally still stand up for animals if you eat meat. Provided you also carry on your 'standing up' for them through to that as well.
All too often people will be outraged at photos/information about various animal cruelty cases - but then still go out and buy caged eggs, since they are cheaper, or by cheap processed meat that has come from other countries with welfare standards well below ours etc.
If you are willing to make informed choices and decisions about the meat you are eating, then that in itself is standing up for animal welfare/rights. It doesn't mean you have to buy the most expensive organic meat out there - but buying british is a huge start - generally we have much higher welfare standards that a lot of countries (even if in some cases out standards are still lower than they maybe should be) but that pushes the price of our meat up. Buying from a butcher, who knows where the meat has come from is also good. Look at food labels - check your eggs are free range, but also check thinks like mayonnaise (where often they will be caged eggs!)
It's like the person who said they pollute, but still care about the environment. It would be hard/virtually impossible to not pollute at all. But it would be hypocritical to go on about the environment if you leave every light in your house on all day, heating on with windows open all day, driving a gas guzzling car every time you leave the house, not recycle at all, gets dozens of plastic bags every time you go to the shop etc etc. But when you are trying to do what you realistically can. then you can prehaps start to point things out to other people and so on.
And I would say it is similar...if you are just saying words about how much you care about animals. It means nothing, if you are actually doing something, then that is different. And imo doing something can still involve eating meat (in reality, humans aren't going to stop eating meat any time soon!), but just do it sustainably, ethically and welfare friendly.
What are the downsides?