Will I get anywhere with no GCSEs?

I’m homeschooled, and I’ll be starting college next year. I was getting ready to take my GCSEs online, when my parents suddenly decided I could do perfectly well without them. Instead, we’re focusing on building experience through… Udemy courses. They seem very confident that a complete lack of GCSEs will not be a problem at all, and that for whatever I want to do I’ll be able to get it by just talking mildly intelligently and throwing a few Udemy certificates at them. Is the lack of GCSEs going to be a problem going forward or are they correct?

Which organisations recognise Udemy courses?

Absolutely no idea

Might be an idea to find out before your educational qualifications go down the toilet?

Well at the very least, English language and maths GCSE are used as literacy/numeracy targets by the government and are not uncommonly expected by employers, or an equivalent (e.g. functional skills qualifications in the same).
Fundamentally you will not be achieving the same benchmarks as the majority of other young people in the country which I think is a concern, as at minimum workplaces are unlikely to accept a udemy course to prove literacy/numeracy in the way a maths/English language GCSE or functional skills qualification would be (thus potentially necessitating you do those later anyway - possibly as an adult learner). Granted in the case of employers I've never had them actually check my GCSE certificates when they ask for those. However also most universities require at least GCSE English language/maths or equivalent, and most apprenticeships similarly expect that level and proof of literacy/numeracy, and universities certainly generally do require you the certificates from your qualifications and aren't likely to accept udemy courses in lieu of a formal academic qualification.
Are you planning to do A-levels or something for your 16-18 education? Or are they just intending to do more of these courses? If you get functional skills/GCSE English lang/maths then somehow prepare the material you would need from GCSE for any given A-levels (or similar e.g. BTEC, IB, etc) you take, and then follow the A-level (or other level 3 qualification syllabus) then that gives you some more options. If their expectation is you just do more "advanced" udemy courses in lieu of those as well then that's really going to severely limit your options to the Open Uni (which has foundation modules for those with minimal/disrupted education or who have been out of education for a long time) or starting in a minimum wage job and hoping to advance from that.
You might be able to do some things with just those courses (retail, food services, similar), although you'll almost certainly need some kind of functional skills English lang/maths at some point even for those things, but not "anything" as your parents seem to believe...?

Okay firstly, what are you wanting to pursue as a career later?
I'm a home educating parent, plus my husband has (as far as he knows) no GCSEs, so I've got lots to say on the subject, but the above question would be a good start.

Politics; I want to be in Government. My parents say GCSEs are outdated, that if I wanted to do A-level Politics for example, an interview or however they are called would suffice. And yet all evidence I’ve seen online has been “significantly limited opportunities for people without GCSEs”.

Okay so your parents are definitely somewhat misinformed. To do A Levels you either have to do them in somewhere like a sixth form / sixth form college, or you can do them as a private candidate in a private exam centre whilst continuing to be home educated post compulsory school age.
If you do them privately then it's true you don't need any GCSEs (but bear in mind it's a very expensive option), but to do them somewhere like a sixth form college then you have to meet their entry requirements. Just having an interview is not going to cut it at all, you will not be offered a place. They do not care that you are home educated, they just care about you meeting their entry requirements.
So the usual entry requirements for A Levels at somewhere like a sixth form college is 5 GCSEs (or IGCSEs) including English Language and Maths, at grades 4 or above. BUT some very competitive sixth form colleges ask for up to 8 GCSEs.
Udemy courses, whilst very useful for teaching you stuff, and still fine for putting on a CV, are not going to be accepted in lieu of GCSEs or IGCSEs.
So unless you do GCSEs, you're not getting into a college type of establishment to do A Levels. Sorry to burst your parents' bubble.
Although you can still do them as a private candidate, as I say.
Now then, that doesn't mean you can't go into politics via a different route rather than going down the A Level path. So let's explore some other options:
Firstly, you could go to college at 16 with absolutely zero GCSEs and get onto a Level 1 course, and work your way up to Level 2, and then finally completing a Level 3 Extended BTEC. You will have GCSE Maths and GCSE English Language incorporated into your time at college, so you will do those whilst you're there.
After that, you would be eligible to go on and do a BA in Politics at a brick university. Looking for example at the University of Manchester, a typical offer would be grades DDD in a BTEC National Extended Diploma.
The downside of starting at Level 1 at college and working your way up is that it'll take 4 years (whereas A Levels take only 2 years), so you'd be starting university at 20 years old rather than 18. Now honestly that doesn't matter at all, but it's still worth bearing in mind.
Another option is doing GCSE Maths and GCSE English at college as a mature student once you are post-19, and then doing an Access to Higher Education Diploma. Once you've done that, you will be eligible to apply for BA Hons Politics at a brick uni.
Alternatively you can bypass any of those requirements by choosing to do a degree with The Open University, which has zero entry requirements. In this case you wouldn't need GCSEs, or anything else, you would just enroll onto the degree course. Your choices within the political sphere are:
BA (Hons) History and Politics
or
BA (Hons) Politics, Philosophy and Economics
Don't assume that a degree from the Open University is of lesser quality than a degree from any brick university, because it absolutely isn't. I'm currently on my final year of an OU degree, and I've been accepted onto a Masters degree at the University of Edinburgh for 2025.
The downside is that you're studying at home though once again, so you don't get the whole "student experience" - i.e. the social side - that you would get from a brick uni.
It boils down to this - if you want the MOST doors to be open to you, then take 5 GCSEs including English and Maths, however it absolutely does not mean that you cannot pursue Politics if you don't take them, it just means that you have to go through other routes.
But your parents are dreaming if they think you'll be accepted onto a sixth form college course to do A Levels if you have no GCSEs. That just isn't going to happen.

Thank you for the detailed reply! Because of being homeschooled for around five years now without having any real social life (scouts etc didn’t work out) I was very much hoping college would be a chance for me to, well, actually communicate with other people of similar interests and age. However I never really saw a course that interested me in college, and yet again another U-turn was taken when they decided “why not do A-levels?”. I was unaware GCSEs would be necessary for it, and I certainly don’t have time to do five GCSEs minimum in… a year. Not entirely sure what to do atp except wait for the point to prove itself about the GCSEs. Do you think not having any GCSEs would hold me back quite as much as people seem to think aside from just college and Uni? Like, would it also limit jobs etc, because I can’t imagine anyone in Government completely lacking GCSEs, A-Levels, etc?

There is a slight possibility that you may get asked about GCSE English and Maths by future employers, but it's not particularly likely.
Generally speaking, once you have a degree, people tend not to be bothered about GCSEs.
But you can take those two subjects at any age, for free, so I wouldn't worry too much there.
As for a lack of A Levels, these absolutely will have zero impact on your career as long as you go down another suitable path into politics.
Which is your nearest college?

I’m not entirely sure, but I do know there’s a couple to choose from. Nearest is probably Colchester Institute but of course there are a couple other options

Okay so it doesn't look like there's much in the way of relevant courses at Colchester Institute, but having a look in the local area it looks as though The Sixth Form College Colchester has an Advanced Foundation Programme which enables students to get GCSEs if they do not already have them, which is worth checking out:
The Sixth Form College Colchester - GCSE